1)  Symmetra:  Symmetra's Photon shield is Genji's best synergistic allied ability.  Being able to have a regenerating shield is huge for Genji and he greatly benefits from having it on him.  Since Genji usually takes a lot of small damage shots while parkouring around the map, Symmetra's Photon Shield helps to keep him alive much longer.

Symmetra can put Sentry Turrets around the map, Genji can use these traps to retreat to if he needs to get to a safe spot to be protected.  Symmetra can put these traps in a room with a health pack to keep enemies away from it while allowing offensive allied flankers like Genji a place to go refill up on health safely.

And of course, Symmetra's Teleporter helps all her allies (including Genji) to get back to the fight faster after dying.  Symmetra can also put her Teleporter behind the enemy so that Genji is already in a flanking position.

2)  Ana:  Although it can be difficult for Ana to shoot Biotic Rifle heal shots at Genji from a distance due to Genji's quick abilities like Swift Strike and wall climb, he greatly benefits from well aimed rifle heals from a distance, since other allied healers will have a difficult time healing him with their healing abilities.  Like other offensive allied flankers, it's good for Genji to communicate with Ana to let her know where he is at and if he needs healed.

If timed properly a Biotic Grenade thrown on Genji while he is out flanking can be very powerful when combined with another healing source such as Zenyatta's Harmony Orb or Lucio's heal aura.

One of the biggest synergies between Ana and Genji is how effective Ana's ultimate Nano Boost is with Genji's ultimate Dragonblade.  I have Dragonblade listed as the best synergistic ultimate for Ana to Nano Boost.  Normally Genji is vulnerable while using his ultimate but with increased speed and damage reduction he has little to worry about and will be able to attack enemies much more effectively while Nano Boosted.

It's usually a good idea for Ana to throw a Biotic Grenade on a Nano Boosted Dragonblade to help ensure Genji's survival further while using it.

3)  Lucio:  Lucio's speed and heal auras work wonderfully with Genji.  Being able to move faster and get healed while out attacking is huge for Genji.  Since Lucio's auras only have a range of 30 meters, it's important to make sure the two of you stay somewhat close in order to make this synergy work smoothly.  Lucio's auras also only work when the two of you keep line of sight with each other, which can prove to be difficult to achieve sometimes due to Genji's nature of moving through rooms/hallways to flank enemies from behind.  You may need to communicate with Lucio to let him know what you desire more (either healing or speed) while out flanking and harassing.

Lucio's Soundwave (knocks enemies back) can help Genji by knocking back enemies that Deflect does not work on, such as Winston and his Tesla Cannon, Mei and her freeze gun, Symmetra and her Photon Projector, and Zarya's Particle Beam.

Lucio's Sound Barrier ultimate pairs well with Genji's Dragonblade as it will keep you alive more efficiently while using it thanks to the temporary shield.

4)  Zenyatta:  Zenyatta's Discord Orb can make Genji's work much easier since all your attacks will be amplified by 50% on the target who has the Discord Orb.  Zenyatta's Harmony Orb can be effective on Genji, but since Genji usually wonders around too far, he usually loses Zenyatta's line of sight for it to last long enough to be of a huge importance.  If you get the Harmony Orb from Zenyatta, try to stay within his line of sight if you can to gain the extra healing from it.

Zenyatta's ultimate Transcendence actually works very well with Genji's Dragonblade ultimate as Genji is usually very vulnerable while using it, but with Transcendence you don't have to worry too much about getting hurt while using it.

5)  Mercy:  It's hard for Mercy to keep up with Genji and it's generally not safe for Mercy to follow a Genji around since Genji is usually off on his own harassing the enemies from all angles.  A Swift Strike can leave Mercy hopeless sometimes with no one to fly to.

Unfortunately Mercy's Resurrect is usually out of Genji's range, and there are many times where Resurrect does not work on Genji simply because of his nature of going too far away from his team.

1)  Zarya:  Genji is usually in a great position to take advantage of Zarya's Projected Barrier, since he is usually in the front lines harassing and ambushing the enemy.  A Projected Barrier also works great for protecting Genji when he is using Dragonblade.

Be careful when Zarya uses Graviton Surge, as getting up close to the clumped up enemies with Dragonblade is still a very risky endeavor for Genji since the enemies can still fight back while in the surge.  Only consider getting up close if you can get a Projected Barrier on you, or some kind of protection.

2)  Winston:  Winston has the capabilities to keep up with Genji thanks to his Leap ability.  Winston can Leap where Genji is at and then throw down a Barrier for protection, which can also help protect Genji while he is using Dragonblade.

3)  D.va:  D.va also has capabilities to keep up with Genji thanks to her Boosters.  D.va can knock down enemies with her Boosters that Deflect does not work on (like Mei, Winston, Symmetra, and Zarya).

She can protect herself and Genji with her Defense Matrix ability, which could allow Genji to safely use his Dragonblade without too much harm.

D.va can use a Self-Destruct to scatter enemies around giving Genji an easier opportunity to pick off fleeing enemies.

4)  Reinhardt:  Reinhardt's shield is not very useful with Genji due to the fact that Genji mostly roams around on his own and is usually not near Reinhardt to take advantage of his shield.

Reinhardt's ultimate Earthshatter can allow Genji to safely use Dragonblade to finish off the knocked down victims.

5)  Roadhog:  Roadhog is an independent tank that doesn't have many synergies with Genji, although Roadhog's ultimate Whole Hog can scatter enemies around giving Genji an easier time to pick off disoriented enemies from the knock backs of Whole Hog.

1)  Widowmaker:  Genji's distractions can enable Widowmaker to do her dirty work from afar without being targeted as much.  Widow's Infra-Sight helps all her allies, and with Genji it can help track down fleeing enemies, allowing you to get a Swift Strike in to finish a victim off.  Infra-Sight can also enable you to start firing shurikens before an enemy comes around a corner.

2)  Torbjorn:  Torbjorn's Armor Packs are very useful to Genji as it can allow him to absorb more damage before needing healed, this keeps Genji in a flanking position more often.  However, Armor Packs are not as useful as Symmetra's Photon Shield, since it does not replenish itself, as you will have to pick up a new armor pack to gain more armor again.

Torbjorn's turrets can allow Genji to retreat from a losing battle quicker by getting in the line of a turret's sight, thus keeping enemies away from you while you seek healing.  You can also possibly lure enemies into Torbjorn's turrets as well.

3)  Soldier 76:  Soldier 76 can put down Biotic Fields, which you can go to if you need some extra healing.  The problem is that Genji is usually off on his own and away from Soldier 76 for the most part.

Soldier 76's ultimate Tactical Visor can make enemies run and hide, which can be a good time to activate Dragonblade to chase the enemies from hiding away.  You can also help protect Soldier 76 from getting attacked while he uses Tactical Visor with a Deflect.

4)  Mei:  Mei can freeze targets with her freeze gun, giving Genji an easy opportunity to finish off those victims with shuriken headshots.

Genji can climb Mei's Ice Walls, which can give Genji more possibilities for mobility to get around the map.  Genji can also climb to the top of an Ice Wall and attack enemies from unexpected angles.

Mei's ultimate Blizzard is a great opportunity for Genji to use Dragonblade to finish off all the "chilled/frozen" targets.

5)  Pharah:  Pharah can use her Concussive Blast to knock back enemies away from Genji that Deflect does not work on, such as Mei, Symmetra, and Winston.

Before Pharah activates her Barrage ultimate, Genji can get right in front of her to use a Deflect to protect her while she is Barraging.

6)  Junkrat:  Genji can help lure enemies into Junkrat's Steel Traps.  Junkrat's grenade spam can help pave the way for Genji to traverse certain parts of a map.

Junkrat's ultimate Rip-Tire usually makes enemies flee away from it, which can be a decent time to also activate Dragonblade to slice away at the scattered enemies.  You can also get in front of the Rip-Tire and use Deflect to help keep it alive.

7)  McCree:  Together, McCree and Genji can be a decent team.  McCree's Flashbangs can enable Genji to get some easy hits in.  Genji's Deflect can protect McCree while he is using his Deadeye ultimate.  Simply get in front of McCree while he is revving up his Deadeye shots and the enemy will be highly inclined to fire at McCree during this time, so you can Deflect a lot of bullets right back at the enemy making it faster for McCree to line up a shot in return.

8)  Hanzo:  Hanzo's Sonic Arrow can help Genji track down fleeing enemies, allowing you to Swift Strike to finish a victim off, it can also enable you to start firing shurikens before an enemy comes around a corner.

Hanzo's Dragonstrike ultimate can scatter enemies around giving Genji an easier opportunity to pick off fleeing enemies, and especially combined with Dragonblade.

9)  Bastion:  Bastion can provide a hefty DPS, and for any enemies that live/escape it will probably be almost dead and very susceptible to Genji's Swift Strike or Shurikens.

Genji is also a good counter to a Widowmaker, which happens to be one of Bastion's most troublesome enemies to deal with.

Tank Form combined with Genji's ultimate Dragonblade can be a very powerful force together.  For any enemies that survive a cannon ball shot, Genji can finish them off with a slice from his Dragonblade.

10)  Reaper:  The main use a Reaper has with Genji is that if you are being attacked by enemies that can bypass your Deflect (Mei, Winston, Symmetra, and Zarya), an allied Reaper can come by your side to help take those enemies out, especially with his ultimate Death Blossom.

Reapers in general serve similar purposes as Genji, and the two combined will have double the flanking and ambushing power together to take out snipers or other strong defenses.

When Reaper uses his ultimate Deathblossom, Genji can protect him with a Deflect, by blocking off enemies from a distance.

11)  Tracer:  Like Genji, Tracer is mostly an independent flanker and harasser.  Together they can spell disaster to strong defenses like Widowmakers and Bastion Sentries.  Besides providing double the confusion and harassing power between the two heroes, there's not much else worth mentioning.