Identity Absorption

Bob's got the power to perform a Fusion Dance with other people, with or without their consent. When he does, he takes from them their personality and memories. Whether or not the people live on inside his own mind varies from work to work. Generally speaking, this sort of thing kills the absorbee, although exceptions exist.

Of course, taking others' personalities and memories can lead to problems- Occasionally, Bob has a Loss of Identity due to remembering things or behaving the same way that Alice, Carol, Dave, Eva, Fred, Gina, Harold, Irene, Johnny, Kim, Leon, Melissa, Nick, Ophelia, Pat, Quinn, Rolf, Stella, Travis, Ursula, Viktor, Winona, Xavier, Yolanda, and/or Zack did, in addition to his own identity.

Compare Mental Fusion, where both Alice and Bob are still alive, but a mental link is formed between them.

See also: The Assimilator, Power Copying, Transferable Memory, and Memory Gambit.

Anime and Manga

 * In Baccano!, when an immortal is devoured by another, the surviving immortal gains all the other's memories.
 * The novels later give us
 * Hellsing's Alucard keeps the memories of all those he devours.

Comic Books

 * X-Men's Rogue has this as her mutant power.
 * Multiple Man is capable of doing this to his duplicates, should they go off and live their lives away from him.
 * The Superman villain Parasite has this. Usually it's a temporary awareness of their memories, but on one occasion he absorbed a scientist and found himself Sharing a Body with them as "Doc Parasite".
 * In Grant Morrison's Doom Patrol comic book, there is a supervillain called Fog whose power is pretty much this. He can swallow people alive, but all of the people he's eaten still exist as different personalities inside him, and they're constantly arguing with him and with each other.

Literature

 * Wild Cards had early Ace Brain Trust, who worked with the Exotics for Democracy by entering hostile situations and duplicating the minds of political and scientific geniuses. The first time her powers manifested, she nearly went mad, and needed the help of Doctor Tachyon to create mental constructs to filter out each personality --

Live-Action TV

 * The Highlander franchise, from which Baccano took the idea of immortals killing each other for memories, personality traits, and power.
 * In Star Trek: The Next Generation, Data downloads his daughter's memories into himself after she breaks down.
 * The Borg do something like this, in particular with Picard in "Best of Both Worlds", but the victim is generally subsumed by the sheer number of existing drones and the willpower of the Borg Queen herself.
 * Olivia absorbed John Scott's memories in the 1st season Fringe.
 * In season four a serial killer absorbs the happy memories of his victims which destroys their brains after a while.
 * In Kamen Rider Kabuto, the Worms take on the memories as well as the forms of their victims before killing them. (Not that killing them triggers this, but it is their MO.) More than one has said things to the effect that the person they mimicked would live on in them so killing the original was no loss. We even get two instances of Worms forgetting they're not the person they imitate, prompting an "are all Worms evil or can some gain humanity over time?" debate.
 * In the second season of Haven we find out that  actually has all the memories and the personality of   up to the point that they act almost identically and use the exact same phrases when placed in similar situations. She does not remember who she was before this happened. We later find out that the same thing happened about 30 years ago with   and might happen every time the Troubles come back.
 * The first season had a shapeshifter who could absorb a person's memories and assume his/her appearance while also retaining its original memories. This process normally kills the victim.

Tabletop Games

 * A dark spell mastered by the evil wizard, Fistandantilus, in the Dragonlance series, allowed him to absorb the youth and vitality of another - thus granting himself quasi-immortality. When Raistlin tricks him and turns the spell back at him, seeking to thus absorb his knowledge and power, the result seems to be something of a Fusion Dance, and when the smoke clears... it's somewhat unclear who actually won. Raistlin is personally certain that he is, in fact, Raistlin, but when he later runs into the All-Seeing Historian Astinus, he refers to him as Fistandantilus, claiming to have carefully recorded the battle and the outcome. Assuming he is right, Fistandantilus actually did manage to absorb Raistlin's spirit, but was overpowered by his mental strength and unbreakable personality, ultimately becoming subsumed.

Video Games

 * In SaGa Frontier, when either Blue or Rouge kill the other, he gains the other twin's personality, memories, and knowledge of magic.
 * Alex Mercer in Prototype does this, and can perfectly mimic people he's absorbed, right down to their voice. He even does it so well that

Web Original

 * Red vs. Blue has the AIs personalities that do this, though technically they were a whole personality to begin with. They form together, absorbed into the Epsilon fragment's mind.