The Buu saga liked to play with this. For starters, the Fusion Dance merges two fighters' personalities as well as their appearances. After that, Buu is absorbed by his dark side, but the new hybrid form is restrained from killing some people due to his good side's influence... Somepeople.
In Mobile Suit Gundam 00, Allelujah Haptism temporarily merges with his violent Split Personality Hallelujah Baptism to becomes "the Super Soldier" with the piloting skills of two men, or as fans call him, "Doublelujah." This is visually demonstrated by the fact that Allelujah always has his right eye covered by his hair, while when Hallelujah takes over, he sweeps the hair over to cover his left eye instead. When both personalities work together, both eyes are exposed (and he speaks with both voices and personalities in turn).
Similar situation with Une in an earlier series, Mobile Suit Gundam Wing. Lady Une has two personalities, "Iron Une", a cold-hearted and ruthless military commander and "Saint Une", who is kind and gentle but ineffectual. She spending about half the series in a coma and wakes up a couple of episodes before the finale, having resolved the conflict and now combining the military skill with the compassion.
Houshin Engi has this with Taikoubou and Ou Eki. They later merge together to become Fukki, although Taikoubou is the main, dominating personality.
Zigzagged a bit in the anime ending of MÄR. Snow was a clone created from a piece of Koyuki's soul. Making them not so much split personalities so much as original and copy. In the end, Snow merges back into Koyuki to become one whole person to be with Ginta on Earth. The ending seems to indicate a complete merge of both sets of memories, while retaining the same personality. It helps they essentially acted as the same person anyway.
Change 123 is all about trying to merge the personalities of Motoko and HiFuMi and Zero.
Often overlooked in the English dub of Yu-Gi-Oh!, Yugi and the pharaoh usually combine their minds when dueling. The reason this is overlooked is because Yugi merged with the pharaoh looks pretty much exactly like the pharaoh all by himself. On account of the pharaoh looking like an older version of Yugi.
In Yu-Gi-Oh! GX, this occurs during his final duel against Yubel when Juudai accepts that he is Haou, the Supreme King, and no longer fears or denies that power.
In Bleach, Ichigo's power manifested in the forms of Zangetsu, his Zanpakuto, and his Inner Hollow. In time, he comes to dominate both of them, learning how to use their power for himself. He also tends to take on aspects of their personality and appearance when using their power, such as the coat he acquires in Bankai mode and the mask and personality changes that accompany his Hollowfication. Recently, Zangetsu and the Inner Hollow merged themselves while Tensa Zangetsu was trying to teach Ichigo the Final Getsuga. The result seems to be Tensa Zangetsu wearing a white robe instead of a black one, and having the top part of the Inner Hollow's super evolved mask. However, his personality seems to remain as that of Zangetsu's. Ichigo then merges with THIS personality, and takes on its confidence and... moodiness.
In Magical Project S, Misao becomes a lot stronger mentally when she accepts her Pixy Misa Dark Magical Girl persona. (And has full control when turning into Pixy Misa later.)
Hikaru and Nova in Magic Knight Rayearth, when Hikaru comes to realize Nova was created from Hikaru's feelings of guilt and regret for killing Princess Emeraude, and finally learns to accept these feelings and forgive herself.
X-Men: Professor X's wayward son Legion had his personalities integrated... into one guy who was far worse than his previous selves put together. The result was the Age of Apocalypse.
The Green Goblin has undergone this after his 1996 comeback, the Goblin previously veering between being an outright Split Personality of Norman Osborn, a psychotic break from reality and the power fantasy of an unstable Corrupt Corporate Executive who just won the Superpower Lottery. Naturally, the amalgation of a mentally ill white collar criminal with his homicidal maniac alternate persona did not exactly make things better- the new Norman Osborn was a Magnificent Bastard who developed particularly twisted views on his emnity with Spider-Man and graduated from millionaire industrialist to head of S.H.I.E.L.D. (because Humans Are Morons). Recently, the Goblin has shown signs of making a comeback, in the form of delusions and homicidal mania.
Death's Head II gained independence after the Minion cyborg assimilated the minds of 105 of the most deadly minds in the universe, only to have its last target (the original Death's Head) take over its programming and form a gestalt personality.
In ElfQuest, Two-Edge's mind was split in two by Winnowill, his mother. He tries to use a troll vs. elf war to decide what he really is. note Significantly, the war is won by the elves AND their troll allies. Later, instead of running, Two-Edge allows Leetah to heal his fractured mind. His later appearances show him to still be a bit loopy, but with only one mind running the show.
Green Lantern has Carol growing more stronger when she accepted the Star Sapphire ring willingly to the point that she regains control of herself in her Star Sapphire form this time.
Occurs to Twilight Sparkle near the latter end of The Immortal Game. Earlier in the story, the psychological trauma of being transformed into Nihilus had caused her mind to split in two — the dominant, peaceful-to-a-fault Sparkle, and the more brutish Twilight. The two personalities spend quite some time arguing, with Twilight pushing for a merge to restore themself to a full and equal mind, but Sparkle being too afraid that Twilight will pull a Split Personality Takeover and be as monstrous as Nihilus was. Eventually, Titan captures Sparkle and tortures her. The pain and desperation causes Sparkle to accept Twilight and fuse back with her, recreating the real Twilight Sparkle. Cue asskicking.
Pops up in Pinkie Pie's reharmonizing chapter: Angry Pie, a Split Personality representing Pinkie's anger, attempts a Split Personality Takeover by absorbing Pinkie and her other personalities. In order to defeat her, Pinkie and Pinkamena fuse together, and the resulting being defeats and absorbs Angry, before fusing with the other personalities, restoring Pinkie's mind to its full state for the first time since she got her cutie mark.
Happens again in the Dark World timeline, but differs from the main universe, in that Twilight has to enter her mind and talk her personalities into doing it, and she didn't have split personalities the entire time; she forced her mind back together and a number of factors resulted in it splitting again, allowing Twilight to help her put it back together right.
Fluttershy and Erica eventually perform this in Becoming Ponies. As do one half of Twilight and Isaac.
The Sum of Their Parts is a fanfic that begins by establishing that Faith (from Buffy the Vampire Slayer) is actually an alternate personality for Daria Morgendoffer produced to handle her rage over her family's brutal murder. Eventually she winds up in a fight with Glorificus who steals the mental energy maintaining their separation. Then Willow pulls the same trick on Glory/Ben. Daria's and Faith's minds work together to become "reason, backed by intuition... more than the sum of her parts," while Glory/Ben become completely paralised by indecision: "less than the sum".
A Shadow Of The Titans: According to the Queen, the longer that Jade spends in Shadowkhan form, the more this process will occur with the two of them, until eventually all that's left will be a being with the Queen's amorality, but with Jade's wit to keep her from being Stupid Evil.
Films — Live-Action
The author and his cartoon character are merged in Monkeybone.
Me, Myself & Irene: "I'm calling the shots from now on, Hank. I don't need you to fight my battles for me. If you can back down from something this important, you're nothing at all. YOU'RE NOTHING AT ALLLLLLLLLLLLLL!"
Fight Club: "You met me at a very strange time in my life."
In Hellraiser III: Hell On Earth, Pinhead Unbound and Elliot Spencer are merged back into the same being, which turns out to be Pinhead. Joey is given just enough opportunity to stab Pinhead and send him back to the Cenobite dimension.
This happens to the main character at the end of City of Illusions by Ursula K. Le Guin.
Dandra and Tetkashtai in the Dragon Below trilogy merged into one person at the end of the second book, combining Tetkashtai's psionic power and academic knowledge with Dandra's stubbornness and mental stability to form one psion much more powerful than the sum of her parts.
Susannah Dean in The Dark Tower. She originally alternated between the personalities of Detta Walker (kind of psycho and seriously badass) and Odetta Holmes (a wonderful person, but often completely useless). Forcing them to notice each other led to them merging into Susannah, who keeps Detta's ferocity and Odetta's kindliness and feelings for Eddie. Still, the merge isn't perfect; at one point, Susannah has to let Detta take over again because she learned a lesson Odetta never did. "Poetry-readin' bitch like her never had the time for a little ars mathematica." Detta is also prone to resurfacing on her own occasionally, but when she does she is much less vicious than she was originally.
The Wheel of Time: Rand Al'Thor suffered a long time clashing ever more obviously with the voice in his head (which could take over his body at times), that of his previous incarnation, Lews Therin Telamon, and finally snapped in a long overdo psychotic break. Eventually he becomes insanely homicidal and then nihilistic, raving about destroying all humanity as everything is pointless. He and his previous incarnation (which as he seemed to be able to take over Rand's body and control of Saidin can be seen as a split personality) reach a kind of epiphany and he manages to step back from the brink. Afterwards the narration makes clear he will never again hear the voice of Lews Therin again, likely because he at last accepted the simple truth, 'that they were not two people, and never had been'.
Robert Sheckley has a story where a man underwent a treatment in his childhood by having his extra personalities siphoned away into artificial bodies. The story is about him searching for them all over the Solar System. In the end, he collects them all, expecting them all to reintegrate into his, only to have all the parts, including himself, merge into a completely different persona.
In the Buffy the Vampire Slayer episode "The Replacement", Xander's personality is magically split into two bodies — one being confident, competent Xander and the other being awkward, pathetic Xander — and then merged again at the end.
In the season 6 finale of Supernatural, Sam is stuck in a Mental World where his identity has split into three personalities: Sam, Soulless Sam, and the Sam who's been tortured in the Cage. Finding his way out of there requires the other two to merge back into him.
Despite providing the picture, Jekyll averts this. Even though Jackman and Hyde agree to work together, they retain their individual personalities and and powers or lack of them. Their alliance is simply a case of switching voluntarily depending on which would be most useful at any time, and both of them agreeing to devote their respective talents towards the common goal of saving Jackman's family.
There's an unusual one at the climax of The Who's Rock OperaQuadrophenia. In "The Rock," as Jimmy's life flashes crawls before his eyes, the musical themes representing aspects of his personality merge into one. Hm? You say I can't possibly get all this information from an instrumental? You're right: It's all there in themanual liner notes.
In another Rock Opera example, Green Day's American Idiot has this happening to St. Jimmy, the evil side of Jesus of Suburbia ("Jimmy died today; he blew his brains out into the bay").
This is a central mechanic of the game, Vox, where characters incorporate the voices in their head as a part of themselves they have 'forgotten,' growing closer to perfection each time.
Changeling: The Lost has an Enemy Without variant with regards to the fetch, an impostor made from a fragment of the changeling's soul to fill their place after they're taken by the Gentry. Most changelings are just content to kill their fetch - either in an attempt to reclaim their life or destroy one of "their" tools - but it's possible for a changeling and a fetch to come to a deep, intricate understanding of how each one reflects aspects of the other's personality and being. If that happens, the changeling and fetch merge into one being, with the changeling's Clarity going up a level. Keep in mind this is a long, difficult process, and odds are other changelings won't look on you so kindly for attempting it...
With the ubiquity of Brain Uploading in Eclipse Phase it's not uncommon for people to make temporary copies or "forks" of themselves and later reintegrate the two. Unfortunately the longer they remain separate the more likely the chance of integration causing stress.
And in Birth by Sleep, it's revealed that Ven also merged his heart with Sora's heart and in fact had been in him throughout almost his entire life and all of the Kingdom Hearts games long before Roxas and Xion came into being. However it might not be the case here since Sora's really only holding his heart for safe keeping and isn't receiving anything from Ven. However, if what the endings of coded and Birth by Sleep seem to be implying are true, the merges are only temporary, and the plot of the upcoming games will most likely focus, in part, on giving Ven, Roxas and Xion their own bodies.
This is finally brought up in 3D, with Xemnas asking Sora "The bits and bytes that have made up your life so far... can you say for sure that they are not just copies of someone else's?"
Not quite a merger, but in Vampire: The Masquerade – Bloodlines, in the climactic dialog with Jeanette/Therese, with high enough stats you can persuade them to make amends and tolerate each other, in which case they bury the hatchet and peacefully coexist. Speaking with them later on reveals they're still separate entities, but apparently much more aware of each other and the ensuing character is named 'Tourette' by the game.
Fei in Xenogears merges with no less than three (possibly four, though that one was an Empty Shell) alternate personalities after convincing them to. This is remarkable since he wasn't the original, but the third personality.
In The Darkness videogame, Jack Estacado manages to control the Darkness, a demon spirit that existed in his family since WWI, not through guns but by absorbing it into his own spirit. This allowed him to control the Darkness, but the Darkness reminded Jackie "with each life you take. I grow closer to owning your soul!" Guess what he has to do next to reach his Uncle Paulie?
Even Death is not enough to escape: Jackie commits suicide after Uncle Paulie kills his girlfriend before his eyes while he's being restrained by the Darkness itself, but comes back with the Darkness still possessing him.
In the Warcraft storyline, the first Lich King, Ner'zhul, has mostly total mental control over all the undead. He chooses his Champion, Arthas, to be the host of his soul which has been trapped in the frozen throne. It could be argued that Arthas's taking of the title of Lich King is one of these.
It's not fully explained, but this happens in the Dimensional Vortexes in the DS re-release of Chrono Trigger.
In the Fallout: New VegasDLCDead Money, with a high enough Speech skill you can do this to God/Dog to deal with him peacefully at the end, with the new identity forgetting all that has happened to him. Notably, if you were nice to them previously, Dog will regretfully say that he doesn't want this to happen because it will mean forgetting you.
The goal of the Meta (a gestalt entity of AIs created as Literal Split Personalities) in Red vs. Blue: Reconstruction is to reconstruct the original Alpha AI from which they were split off. According to Word of God, the first AI in the Meta (Sigma) intended to rebuild the Alpha with itself as the leader.
The Doctor Who comic The 10 Doctors demonstrates a rare version of the trope. As the title suggests, the Doctor's regenerations 1 through 10 all band together to save the universe. At one point, Ten gets captured by the Daleks and is brainwashed into "Dalek Tor". In order to defeat the programming there is a Battle in the Center of the Mind where the Doctors all form one persona — an amalgam of his multiple personalities.
Mingmei Wu and Professor Sorgaz in The Wotch, once Mingmei is made aware of her status as a gender bent teacher dunked in the Fountain of Youth and the origional personality reappears. Perhaps a slight twist on this trope, as well; Mingmei is perfectly willing to go away so Professor Sorgaz can return to his normal life. It is Sorgaz who proposes merger, claiming she already has a better life than he ever did (He proposes merging the best of both worlds— her friends, his bank account).
This is one of the possible explanations for the ending of the Aiden and Brownwyn arc in Misfile. It wasn't made terribly clear, but Rumisiel did force the Wraith-thing to into Bronwyn's psyche and told it to stay there, and Bronwyn did regain her affection for Aiden as a result.
Inverted: Gamzee Makara begins with the stable merged personality when stoned. Then he sobers up, the personalities splits, and both of the resulting personalities are Ax-Crazy.
When Jade Harley ascends to the God Tiers, she's merged with her dream self which had branched off into its own different personality, Jadesprite, for a time.
This apparently was to be the destiny of Calliope and Caliborn and it is implied to be part of the natural lifespan of their race, the cherubs. Sadly Caliborn managed to kill Calliope's dream self meaning that they will remain as fractured personalities forever.
Attempted a few times by Jix and her alternate personalities Remula and Lamerix. The first time it seemed to work for a while, but broke down when she was cloned and Remula was seemingly transferred to the clone they were actually copied. Another time a psychologist tried to get her personalities to destroy each other.
Happens to Sasha and Abby when Sasha dies while mentally linked with Abby in the Metamor City novel Making the Cut.
Mike in the Total Drama All Stars finale, after hitting the Reset Button, not only loses his other personalities, but also gains the abilities of his other personalities, except for Mal's.