In the Deckard Cain Meta Tier List made by @Oxygen, @MagikMurlok asked if someone could compile a list of Heroes that have strong self-sustain that can be viable in matches that features no Supports. I decided to help.
I ended making a list of all non-Healer Heroes that have any form of self-healing. Took me around 6 hours to compile every single nook and cranny (with all the revisions and edits), so here it is! I hope this help. Any feedback is welcome.
I've also included a suggested build for each character to use in the event that there is no Healer in the team, aimed at maximizing survivability.
Special thanks to @ExorionAether for the help with talents and Heroes I missed, forgot or did not include originally for other reasons.
Heroes are organized in alphabetical order. Press the "reveal hidden content" button to reveal the lists.
 
MELEE ASSASSINS
RANGED ASSASSINS
BRUISERS
TANKS
SUPPORTS
TOP 10 BEST PUBSTOMPERS WITHOUT HEALER
Deathwing: since he cannot be targeted by buffs and heals from his allies nor debuffs from his enemies, Deathwing is a powerful candidate for teams without healers. All his level 1 talents are aimed at self sustain, and he also has some few other defensive talents; while you'll be sacrificing damage for survivability, Deathwing will still pack a punch. Fenix: as long his Shield doesn't drop completely, he has one of the most powerful lane presences in the game, essentially having two healthbars. And if losing his Shields he can simply retreat and let them replenish again. Just be careful with hard engages, stuns and damage-over-time (as each tick will put Shield Capacitor on cooldown). Malthael: ridiculous sustain that allows him to 1v2 or even 1v3 under the right circumstances. Make sure to hit as many opponents as possible with Basic Attacks to maximize his sustain. Dehaka: incredibly sticky and slippery, with a global presence that allows him to engage and disengage at ease. His trait combined with Adaptation makes him really hard to kill. Blaze: powerful lane presence and one of the best self-sustains in the entire game. Diablo: his recent rework made him absurdly resilient, with a self-sustain that can surpass Blaze's under the right circumstances. Sonya: still one of the strongest solo laners in the game, with reliable self-sustain, great damage overall, and strong engage potential. Medivh: with a very versatile kit, he can provide damage, mobility, vision, crowd-control and most importantly, damage immunity and healing. ANY team without a Healer greatly benefits from Medivh. Yrel: the only non-Healer in the game that can directly heal other characters with Gift of the Naaru and Word of Glory, making her a powerful emergency off-healer. ANY team without a Healer greatly benefits from Yrel, assuming she picks those aforementioned talents. Thrall: very strong on really long matches, as his most powerful quest talents require a lot of farming. At the endgame he deal eye-watering damage while healing for huge chunks of health. THE TOP 5 BEST SELF-SUSTAIN TEAM COMBINATIONS
Deathwing, Medivh, Stitches, Kel'Thuzad, Kael'thas. Deathwing, Medivh, Garrosh, The Butcher, Kel'Thuzad. Deathwing, Medivh, ETC, Fenix, Kel'Thuzad. Deathwing, Medivh, Johanna, Cassia, Fenix. Deathwing, Medivh, Yrel, Raynor, Thrall.

As a Ana enthusiast (she pratically became my main over Deckard and Auriel, specially after the rework), I absolutely love trying out combos with Nano Boost. In a similar fashion to my Auriel's Best Hope Bearers topic, this list aims to rank my personal experiences with Nano Boost (as well Nano Infusion) and the best Heroes to use it with.
Heroes that already have some sort of cooldown-reduction talent will often work wonders with Nano Boost, as their effects stack.
This guide will be updated constantly as new Heroes are launched and/or existing Heroes are reworked in a way that affects their DPS.
Cho'gall: unsurprisingly, Cho'gall is arguably the best candidate for Nano Boost as it affects both Cho AND Gall, meaning they can use their already low cooldown abilities much faster, and with greater impact. Under the effects of Nano Infusion, Cho'gall is pratically unkillable, specially if Gall has picked Shadow Bolt Volley with the Shadowfury upgrade, resulting in a massive self-sustain. Malthael: given Soul Rip's very low cooldown, Malthael can madly spam it while under the effects of Nano Boost, melting everything. He can become pratically unkillable by using Tormented Souls (with Reaper of Souls) combined with Nano Infusion, with an uptime almost matching Nano Boost itself (even more if he manages to kill Heroes while under it, thus resetting the duration). Jaina: can annihilate the entire enemy team with Nano Boost in mere seconds, specially when combined with Icy Veins and Ring of Frost. Chromie: with Nano Boost, Chromie can destroy even high health tanks with her combo combining Temporal Loop and Blessing of the Bronze, allowing her the to achieve the highest cooldown-reduction rate in the entire game. Kael'thas: in a similar fashion to Jaina, he can deal nasty damage with Nano Boost, particularly with Living Bomb. Pyroblast can one-shot low health Heroes while Nano Boosted. Kel'Thuzad: can one-shot most enemies with his combo when Nano Boosted. If the conditions are right, he can use his combo up to two times before Nano Boost ends. Sonya: has a lot of potential under Wrath of the Berserker, which, combined with Nano Boost AND Nano Infusion, can make her more destructive than Malthael. However, Sonya requires to be really close to deal damage consistently, and unfortunately she can be kited easily, which is why she ranked lower than Malthael. Tassadar: following his rework, he became a powerhouse, being able to deal absurd amounts of damage with Shock Ray, and if built into it, he can use it even more consistently through Nano Boost. Sylvanas: after her rework, Sylvanas became a deadly mid-range Assassin that can deal surprisingly high burst damage with the proper build, making her a fantastic candidate for Nano Boost. Genji: even after the nerfs to this combo a long time ago, it still is a very powerful one, assuming Genji has enough crowd-control by his side to make the fullest of Dragonblade. Greymane: can deal massive damage regardless of his build. Nano Infusion also provides Greymane with very needed self-sustain, which is his greatest weakness. Gul'dan: can spam Fel Flame like crazy under the effects of Nano Boost. If the circumstances are right, he can use Corruption up to three times or more before Nano Boost ends; assuming Bound by Shadow is taken and he hits as many enemies as possible with Fel Flame. Valla: being a hybrid of basic attacker and spell damage dealer, she can deal surprisingly high damage under the effects of Nano Boost regardless of her build, although her Hungering Arrow can be relatively easy to avoid. Cassia: can make a mess with Nano Boost regardless of her build, although she is particularly more effective with the Lightning Fury build with Ball Lightning. Zeratul: absurdly high burst that becomes even more insane under the effects of Nano Boost. Not ranked as high as other Assassins because he requires a LOT of skill to make the fully use of Nano Boost. Li-Ming: innate cooldown resets upon takedowns combined with already low cooldowns makes Li-Ming a beast under the effects of Nano Boost. If the circumstances are right, she can spam her abilities like crazy. However, her skillshots are relatively easy to avoid. Mephisto: innate cooldown reduction on his abilities due to his trait, Lord Of Hatred, makes him a fantastic candidate to Nano Boost. However, much like Li-Ming, he is ranked lower than the other "mages" because he can not guarantee to get many resets in succession. On the other hand, Consume Souls (with Consumed by Hatred) can potentially wipe the entire enemy team. Orphea: quick resets on Shadow Waltz combined with strong sustained damage makes her a good candidate for Nano Boost, however she falls in a similar category as Li-Ming, since her skillshots are relatively easy to avoid; plus she is a mid-range "mage", which makes approaches harder. Qhira: can deal a huge burst damage with Blood Rage and either Heroic Ability, making her a viable candidate for Nano Boost. Azmodan: when fully stacked, Azmodan can decimate the entire enemy team with a Black Pool-infused Globe of Annihilation while under the effects of Nano Boost. He is not ranked so high, however, because his cooldowns are very long, resulting on him not making full potential of the 8 second duration of Nano Boost, even with 150% recharge rate. Kerrigan: in a similar fashion to Greymane, can deal massive damage in seconds, and Nano Infusion makes her even more durable. However, she is ranked lower than him because her combo requires proper setup to work. Thrall: he falls in a similar category as Sonya, as he can deal a lot of damage but can be relatively easy to kite, making his usefulness under Nano Boost not the best one, but still very powerful, specially with the Chain Lightning build. Alarak: low cooldowns and obscene damage output with high stacks of Sadism makes Alarak a fantastic candidate for Nano Boost, allowing him to deal eye-watering damage. Junkrat: with the Frag Launcher build, Junkrat can deal A LOT of damage when Nano Boosted. He is ranked low, however, because his grenades are easy to avoid. On the other hand, RIP-Tire can really make a mess. Ragnaros: much like Kerrigan and Sonya, he must be really close to deal proper damage, but can deal a lot if given the chance, making him a potential candidate for Nano Boost. He cannot be Nano Boosted while on Molten Core, and will not retain its effects if he gets Nano Boost and then activates Molten Core. Zul'jin: with the Twin Cleave + Guillotine build, he can deal a LOT of damage in quickly succession. However, given the high cooldowns of both abilities, as well the condition of requiring lower health to deal maximum damage with Guillotine, he doesn't work as good under Nano Boost compared to other characters. Maiev: while she has a lot of potential under the effects of Nano Boost because of her Fan of Knives resets, she needs to hit at least two Heroes with it, making the combo more situational. Fenix: while being mostly a basic attacker, he can deal surprisingly high damage with Plasma Cutter, and both his Heroic abilities become even more dangerous with Nano Boost. Murky: can become ridiculously hard to kill with the Slime build + Living the Dream + Fish Tank. Combine that with Nano Infusion, and the murloc can go on a rampage! Not ranked so high because of his low health.

I've been a Healer main since I started playing this game, and Auriel is one of my favorites. Even though we have Deckard, Ana, Anduin and other powerful Heroes in this class, I still consider Auriel one of the best Healers in the game given her very strong lane presence given the fact she doesn't use mana as resource, therefore being able to stay in battle as long she has someone to provide energy through her trait, Bestow Hope. Also, the fact she can endlessly increase her own energy with Reservoir of Hope can potentially turn her into the strongest healer in the game, in terms of raw healing output.
Ever since her launch, I have been testing Auriel's energy generation with a huge batch of heroes. In general, Ranged Assassins are often the best candidates. With that in mind, I decided to compile a list with the Top "Hope Bearers" in the game to give her that sweet energy.
_________________________________________________________________
This guide will be updated constantly as new Heroes are launched and/or existing Heroes are reworked in a way that affects their DPS.
This is the build I currently use, by the way.
Cho'gall: the uncontested champions to provide energy to Auriel. They are a huge lane presence, combined with 8 skills in total makes them a fantastic pair with Auriel to generate energy in double. While they lack the burst of other heroes, they will be constantly dealing damage thanks to their low cooldowns and combined abilities, which will translate in energy really fast. The Cho'gall + Auriel is often a powerful combo even in rankeds, although rarely picked. Lunara: a skillful Lunara player will know how to spread her poison among various targets, giving Auriel a healthy sustain in energy, becoming much stronger at later levels. Raynor: even after his nerfs, he still is one of the best Heroes in the game for sustained damage and situational burst, which translates into energy for Auriel really fast.  Fenix: high sustained damage and exceptional poke makes Fenix a really good hope bearer, specially since his high self sustain through his shields allows Auriel to focus her heals on other allies. Valla: a combination of high burst damage and sustained damage, which makes her a fantastic source of energy, regardless of her build. Tassadar: the recent rework turned him into a powerhouse, with massive burst damage. A single Shock Ray that hits an enemy can fill over half of Auriel's energy gauge, and that's without the quest talent. In addition, with Force Wall being baseline now, he can create obstacles that Auriel can use to stun her enemies with Detainment Strike. Kael'thas: high AoE burst. Living Bomb is specially powerful since it can easily spread to other targets in chains. Phoenix is specially useful to generate energy as well when defending objectives. Sylvanas: given the right circumstances she can surpass Lunara in energy generation, if she follows the Shadow Dagger build and gets enough stacks. Gul'dan: combines the best of both worlds: spike damage and damage over time. The low cooldown on Fel Flame makes him a giving constant damage in the form of energy. The damage over time from Corruption is decent to generate hope, but only if it hits multiple targets. Cassia: much like Valla, she has a bit of everything: burst and sustained damage. If she hits at least two blinded enemies with Fend your energy will skyrocket. While the recent rework nerfed her damage in the early game, she can more consistently provide energy in the late game. Hanzo: long range poke that makes him pretty reliable for getting energy from afar. In specific maps his Scatter Arrow is insane for energy generation. Chromie: huge damage spikes with her skillshots. A Chromie with good aim for Sand Blast will fill the gauge really fast. Dragon's Breath is absolutely fantastic as well and will often max the gauge in one go if used on a crowd of Heroes + minions/structures. Sgt. Hammer: while in Siege Mode she can generate huge amounts of energy if positioned correctly. Auriel can also stay near to peel for Hammer with Detainment Strike if needed. Alarak: can potentially become the one of the strongest candidates for Bestow Hope if he manages to get over 150 stacks of Sadism. Other than that, he is pretty solid with a point-and-click poke in the form of Lightning Surge (specially if related talents are picked) and high burst with Discord Strike. Mephisto: very high AoE sustained damage. Lightning Nova can fill the energy really fast if it hits at least two heroes. Consume Souls is fantastic because it provides a global source of energy. Kel'Thuzad: potential for overflowing energy thanks to his eye-watering combos. However, this reliance makes hard to keep her trait on him all the time since he is very cooldown reliant. Orphea: in a similar fashion to Kel'Thuzad, she relies a bit too much into landing her combos to provide consistent energy, but it is still very reliable and above average. Zagara: can provide fantastic pressure with her basic attacks and abilities, with a lot of sustained damage that will rapidly fill energy for Auriel. Since she will most of the time have a Roachling or Hunter out, this translates into more damage. Zarya: her synergy with Auriel is fantastic since neither use Mana as resource, meaning less needs to visit the Healing Well. Zarya's piercing splash damage from her basic attacks also results in constant amounts of small energy that holds really well. Jaina: her potential rivals Kael'thas, with a very strong burst potential. However, this is gated by her very high cooldowns and over-reliance on the rest of the team to setup ideal situations for her damage to flow. However, if you notice your Jaina pops Icy Veins and either of her Heroic Abilities during a teamfight, swap your Bestow Hope for her.  Ragnaros: very high burst damage, although he needs to be in range to do so. However, he can be affected by Auriel's trait even while under his Molten Core. Nazeebo: I absolutely love pairing with Nazeebo for the simple fact he can make Zombie Walls every 14 secs, which is great to stun opponents with Detainment Strike. However, both his meta builds can grant a lot of energy. Malthael: provides a very large sustained damage through his trait. Not as good as Lunara's, though. Zul'jin: potentially the best energy generator for Auriel in the entire game due his Twin Cleaves (specially if talented into) and high damage from basic attacks. However, he is ranked so low because he can only be this fantastic hope bearer once he completes his "You Want Axe?" quest, which is usually late in the game. Qhira: combines damage-over-time with burst, in a similar vein to Gul'dan, being capable of giving consistent damage. The only thing that gates her from being higher is her reliance on Basic Attacks, meaning she won't always give consistent energy; but will do so in long teamfights. Azmodan: massive burst damage once he completes his quest. Ranked so low for similar reasons to Zul'jin. He is also very cooldown dependent (more than Kel'Thuzad), meaning he is unable to contribute with energy at regular basis. However, should you notice he is about to use his globe, put the trait on him. The Butcher: once he completes the Fresh Meat quest, he deals insane amounts of damage fills up the energy with two or three basic attacks. However, since a good Butcher will not engage recklessly, he will only generate energy reliably during Team Battles and skirmishes.

Guild: Dawn of the Dead | http://www.dotd.org   Faction: Horde | Server: Zul'jin (PvE) | Timezone: EST   Current Progression: 8/9M BoD | 2/2H CoS | 8/8M Uldir CE   We've been raiding max size raids continuously since WoW has been released and are the only guild to have done so here on Zul'jin. We have strong leadership, no drama, and plans to keep raiding for years to come. Unlike many guilds, we're not recruiting for the short term, and we don't over-recruit.   Website: www.dotd.org
  Raid Times: Our schedule is 8-11 EST Tuesday, Wednesday, and Thursday.   Needs: We are a small guild, and we expect high attendance. As such, we recruit people to raid, and desire people who can step in and contribute immediately. We don’t recruit people to sit around, so all spots are for raiders who can expect to be in most every raid.   We are currently looking to add skilled and reliable:
Ranged DPS: High: Shadow Priest, Mage Medium: Warlock 1 Healer:
High: Resto Shaman, Mistweaver Monk
 
*ALL exceptional applicants will be considered regardless of the class.   What we ask of you:   Effort: Not all applicants come from highly progressed guilds, and that’s okay, but it does mean that you need to be prepared. We recruit the player, not the gear, but we do ask that you have some current experience. You need to have the best gear available to you with top end enchants and gems where available. You also need to be able to display an understanding of your class mechanics, role in a raid, and ability to learn new fights.   Attitude: It’s a game. We play for fun. How you fit in with the guild is taken very seriously. We’re a bunch of mostly 18-30 guys and girls who have fun playing together. While we have a good time, we also know when it’s time to buckle down and work hard.   Skill: The best way to determine skill is to see you in a raid. Because we don’t wish to have anyone transfer that we’re not serious about, be able to express your knowledge of your class and why you’re an exceptional player who would be an asset and is worth a shot. Gear will come with time. Skill will not. Impress us with your knowledge of your class and gameplay mechanics. Feel free to share any logs, theorycrafting, or other work you've done.   Commitment: We make a commitment to you, and ask you to do the same to us. A raid takes a team of more than 20 individuals working together. We rely on you to show up to raids, research your class and new fights, respect your fellow players, and notify us when you are unavailable. You rely on us for gear, experience, and coordination. It's a large investment of our time to train and gear new players, and we ask the same investment on your part so that we can each benefit.   We have a variety of informational resources available to prospective applicants on our web site: http://www.dotd.org-- please refer to our "Applications" forum for detailed information. Also feel free to visit us on WoWProgresss for more information and kill videos! http://www.wowprogress.com/guild/us/...wn+of+the+Dead   Should you wish to speak to someone in-game, please don't hesitate to reach out to an officer directly, whisper Alloren (Alloren#1606), Xanah (Xana#1662) or Jeare (Jeare#1759).   We look forward to hearing from you soon!  

<Grey Parse> Is a guild forming of former top 100 US raiders on the horde side of Zul’jin. We are looking to keep a 20-man Roster size with 3-5 backups to push content efficiently while having fun! With a 2-night raiding schedule and a 6 hour week we strive for our raiders to be competitive and perform at top levels.      <Current Raid Progression>   6/8M in just 7 weeks of raiding!   <Raid Times> Wednesday 6:30pm – 9:30pm PST                                  9:30pm-12:30am EST Thursday 6:30pm – 9:30pm PST                              9:30pm-12:30am EST     <Raid Expectancy> Knowledge of mechanics before entering raids. Personal accountability & mechanical proficiency. Come to raid prepared with extra flasks, potions, personal food for progression Minimal random AFKs, Disconnects, random chatter, etc. (we want to have fun but still be proficient) High attendance.   <What you can expect from us:> Positive leadership Flasks, food & repairs provided for each raid (once were up and running and farming) An active guild outside of raids; M+ high key groups, sale runs, AP farm, Alt runs and more   <Raid Requirements> 375 ilvl+ Heart of Azeroth minimum of 30 levels with revered.   If this sparks any interest please contact Huncrow @ Huncrow#1313(Bnet) Thug#7516 (Discord) to set up a discord chat or fill out a quick application: https://goo.gl/forms/MdoY4J5M1ZHVyiNg1