Transferable Memory

Memories are a wonderful thing. When you think about it, they kind of make up your whole identity. But, man, talk about limiting! We have to carry them in these lousy meatbag bodies.

Let's use our Phlebotinum to fix that. Memories aren't just things you hold in your head anymore. They can now be deleted, manipulated, sold, backed up in case of death, shared with the world, or kept secret even from yourself.

This trope is most popular as a central issue in a plot and it's easy to see why. Memory manipulation brings some pretty heavy issues to the forefront. Are we people without our memories? By removing them, do we indirectly kill a part of ourselves, or others? If memories are interchangeable, are we really any different from machines who upload and back up data in the same way?

Alternatively, this trope can also be used simply as a clue in a mystery. Being able to acquire a reliable narration of how events actually happened goes a long way toward giving us a definitive answer.

Compare Liquid Assets and Powers as Programs. See also Brain Uploading, where some or all of the subject's personality is copied/transferred along with the memories. May be used in Memory Gambit. This trope can intersect with Ghost Memory if memories from one person are copy-and-pasted into another.

Examples of Transferable Memory include:

Anime and Manga

Kaiba takes this trope on front and center. Only the privileged can afford effective memory treatment, and on many planets the poor sell their good memories (and sometimes bodies) to make ends meet. We're introduced early on via newscast to a group of known terrorists who sabotage memory treatment facilities, but little is elaborated on that topic until about halfway through Kaiba visits a memory theme park. When it closes down, several memories scream to be taken out of their misery as they're forced to remain in a state of not-quite-life-or-death. The elderly patrons Kaiba was with just thought it was All Part of the Show.
In The Big O, memories are a MacGuffin.
In Baccano!, immortals can transfer memories to other immortals by placing their right hand on the recipient's head and willing it. Of course, since this is also the method immortals use to kill each other (the only difference being what you think when you're doing it), most potential recipients aren't willing to take the risk.
One of the Genei Ryudan in Hunter X Hunter can copy her memories into bullets, and then transfer those memories to other people by shooting them in the head (Memory bullets don't inflict physical injuries).
Tsukimiya from Bloody Cross is a Dhampyr who can read people's memories by drinking their blood.

Fan Works

The Harry Potter fanfiction The Ollivander Children has an Obliviator as a main character, who deals with transferable memories as a matter of course.
The Fallout/My Little Pony: Friendship Is Magic Fusion Fic Fallout Equestria makes frequent use of "memory orbs" as a form of Apocalyptic Log. As well as a Memory Gambit by the protagonist.
In the "Steelverse" of A Brane of Extraordinary Women, the identity of James Bond (and presumably the other "00" agents) has been possessed by several generations of agents with the help of a device which imprints previous Bonds' memories upon a volunteer to be the next Bond.

Film

Blade Runner. Rachel is given memories copied from Tyrell's niece to improve her emotional stability.
Eternal Sunshine of the Spotless Mind averts the base concepts of this trope: it features a device that can erase memories, but using what is "technically" "brain damage", "about on par with a night of heavy drinking". Once they're gone, they can't come back. Central to the story are the main characters and assisting nurse who only realize the ramifications of what they're doing after agreeing to the procedure.
Total Recall, as well as its source material We Can Remember It For You Wholesale uses these as a central plot point. The memories in question are intended to give a person the illusion of having had an exciting vacation on Mars without incurring the extreme expense of such a trip. A central plot point is how these memories can possibly have any sense of being genuine if the man who "owns" them knows that they're false- this leads to the movie's central ambiguity as to whether the uncovering of Quaid's secret agent memories is real, or whether they simply must appear to be real to make the memories seem plausible. This differs from other incantations of the trope, where the internal consistency of conflicting memories is rarely at issue, largely because characters know the difference between their implanted memories and their real ones.. Some people consider this a clue that Quaid's experiences are real.
Dr. Schriber of Dark City implants Fake Memories into peoples heads with syringes in Dark City, and we later see him concocting the fluids that make up these memories.
In the Underworld movies, vampires can access the memories of other vampires by drinking their blood. This is used by Vampire Elders to catch up with the events that transpired while they were in torpor.

Literature

Keith Laumer's A Trace of Memory. An amnesiac alien living as a human on Earth must recover the device in which his full memories are stored. He later discovers that on his home planet almost everyone has this problem.
The Yuuzhan Vong from the New Jedi Order can literally manufacture memories. Usuually this is used as a way to learn new skills quickly, but with time and careful application can also overwrite entire personalities. For the latter, though, as it requires a very complex set of memories, it's easiest to just use someone's preexisting ones rather than grow a whole new set, however.
- The gentle Caamasi can make memories of important events into a memnis, an especially vivid memory that can be telepathically transferred between related Caamasi, and which are passed down like family photos. Memnii can also be transferred to Jedi that are good friends with Caamasi, who can use the Force to share them further.
Physical memories appear in the Harry Potter series with the Pensieve. Interestingly, the existence of these objects is revealed a book before we find out about wizards' ability to force their ways into other minds, which requires the use of Occulumency to guard against. It turns out that extracting memories from a person willingly to use later is a decidedly less evil use of these skills. Skilled wizards can draw their own memories out of their heads - they take the appearance of silvery wisps of an almost cloud-like string.
The Rambosian aliens of Jasper Fforde's Nursery Crime series are filled with a fluid that keeps their memories. The keep jars of this fluid, and regularly back them up with newer memories. If they suffer some fatal misfortune, they can be patched up, refilled and returned to life.
A Magic Mirror in The Elric Saga story Elric of Melnibone steals memories from people.
In Animorphs, the Iskoort aliens have a technology that allows them to buy people's memories; and the alien explaining this technology is quick to reassure the Animorphs that they don't lose their own memories, it just means making a copy of their memories. These copies of human memories turn out to be very useful, because it seems that when they force their Omnicidal Maniac enemies the Howlers to experience the memories of a human, this makes the Howlers not only cease to be "pure evil," but it's so much of an impurity that the Howlers's evil master is no longer able to use them.
- The Helmacrons are also really close to this, since their minds are fungible and when one dies, the mind is absorbed by the rest of the group.
- When Jake is infested by the Yeerk that once controlled his brother, the Yeerk's memories of its hosts are dumped into Jake's memory as the Yeerk is dying of starvation.
In Orson Scott Card's Worthing Saga, the cold sleep used to enable starflight has the unfortunate side effect of completely wiping a person's memory. The solution, spheres which record this and replay it into the subject's brain.
Richard K. Morgan's Altered Carbon and its sequels give us the "stack," a cigarette-filter-sized implant at the base of the brain. It contains a complete record of the user's personality and memories, which can be backed up, sent elsewhere, or installed in a new body (aka "sleeve"). If your body dies but the stack is not destroyed, you can be revived. As an added bonus, a human brain is the only thing that can readily make use of the information in a stack, so even if others get access to your backups, they can't view/edit your mind in cut-and-paste fashion. Your memories can only be recovered by creating another "you" in the process. The novels come complete with a very large and well-thought-out list of the technology's consequences.
A part of becoming the Empress/Emperor of the Twenty Universes in Robert A. Heinlein's Glory Road is the imprinting of all the memories of all the previous emperors and empresses, which are stored in a device called "The Egg of the Phoenix".

Live-Action TV

The New Twilight Zone episode "The Mind of Simon Foster". A homeless man must sell his memories to survive.
Red Dwarf: "Thanks For The Memories".
This could be said to happen in Buffy the Vampire Slayer, given Angel's explanation that when a person is vamped, the vampire demon gets their memories and body, but not their soul.
- Also, slayers inherit memories of previous slayers, albeit through dreams.
Dollhouse A very central concept, along with the ability to transfer and back up etc personalities.
The third episode of Black Mirror focuses around a device called a Grain. It records memories and is capable or replay with all kinds of features like zoom, crop, reconstruction. You can also share memories with people and there is a black market for people's grains.
A planet visited in one of the last two seasons of Stargate SG-1 developed a device that allowed memories to be copied form one individual and transferred to another, but not altering existing memories or outright deleting them.

Tabletop RPG

Dungeons and Dragons again got one of everything. An item "Thought Bottle" that appeared in Tome of Magic does exactly this. Possible uses as a relatively secure data medium or Memory Gambit prop were mentioned.
- In Forgotten Realms tel'kiira ("elven lore-gem") are memory storage devices used as write-at-will personal logs and spellbooks, normally usable only by elves and worn mostly by nobility. Physically, it's a little gem stuck on the forehead of its wearer, most of the time sunk in and not visible. Ancestral lore-gem worn by generations of heirs of a noble House has a value much like the flag of a military unit: not waved around in vain, and losing it counts as a major disgrace. An elven kingdom that didn't allowed humans into capital knighted a human just for carrying one of these from a dying heir to the new rightful wearer, past their guards. Variants include books of elven advanced magic, secret agents' tools and occasional hybrids with other enchanted gems, up to ioun stones turned into semi-sentient defensive spellgem following the owner.
In Exalted there are several means of memory transfer. The most obvious being the celestial exaltations themselves, given that it is a recycled part of god-soul that holds aspects of all its former incarnations. The other being dream stones and other memory crystals. These can be found in tombs or on the black market (dream stones are apparently nearly as addictive as the Xbox of the gods). Makes sense when you realize that the mortal vessels needed to be brought back up to snuff relatively quickly in order to deal with the Primordials or they'd pretty much be reduced to glittering fodder.
From Wraith: The Oblivion, we get the Mnemoi and their Arcanos, Mnemosynis, the sole purpose of which is to transfer and manipulate memories. In a place where memories are important for maintaining one's existence, the Mnemoi are far from welcome, and are therefore one of the three Forbidden Guilds. In actuality, the Mnemoi are using their talents to store the memories of Charon for his return, and the whole persecuted thing is a ruse. One that, sadly, works a bit too well in the end.
In Nomine has Memory Pearl artifacts which are pearl-like objects that can be used to remove/store memories, often used {especially by demons} to remove inconvenient knowledge from a temporary employee/associate often as part of the terms of employment.

Video Games

A truly bizarre version of this occurs in Kingdom Hearts. Xion is a whole character made out of memories.
Final Fantasy VII: One of Jenova's abilities is copying the form and memories of other beings. Just knowledge of this is used to great advantage by Sephiroth to give Cloud even more psychological problems than he already had.
- If one compares the 'Sephiroth in the reactor' cutscenes of FFVII and Crisis Core, one comes to the conclusion that Cloud has memories of things that happened to Zack when he wasn't there. This makes his accidental identity theft much less embarrassing, since apparently Project S genuinely installed some Zack into him.

Web Animation

In Red vs. Blue: Reconstruction, the Epsilon AI was created from the Alpha AI's memories. Agent Washington eventually receives these memories when he implants Epsilon into his head, providing the catalyst for the series' events.