Amnesiac Hero

Wherein the hero has amnesia. He can't remember a thing, except oddly his own name. Sometimes, although rarely, the hero cannot remember his name. Then an someone has to say "Well, we have to call you something!" and they have to make up a name for themselves. Usually, the Amnesiac Hero:

Has amazing fighting skills, and has no idea how he got them. This makes his origin even more mysterious.
Is found by a handsome/beautiful soon-to-be Sidekick, who helps them on their journey to remembering who they are.
Has a dark and depressing past that they probably don't want to remember anyway.

Amnesiac Heroes are common in RPGs and horror games, and are always the heroes in Ontological Mysteries and Quest for Identity. Even if those plots aren't being used, it's a easy way to get the player up to speed, as they're just being introduced to the setting, while the character lives there and should otherwise know about it already.

Compare You Wake Up in a Room and Selective Memory. Gameplay-Guided Amnesia can be a temporary version of this. See also Easy Amnesia, Laser-Guided Amnesia, and Identity Amnesia. Protagonist Without a Past is where this isn't even addressed.

Examples of Amnesiac Hero include:

Anime and Manga

Alice from Pandora Hearts fits this to a "T". She's the most powerful chain in the Abyss who knows only her name, and she inevitably goes on a quest to find her lost memories (though she soon discovers that she may have forgotten them for a good reason).
Mikage from the manga Torikago Gakyuu is this as well, although he doesn't even remember his name. He's given only the surname "Mikage" by a teacher who promptly reveals to him that he is from a parallel world.
Kirika Yuumura from Noir.

Comic Books

Lady Mechanika
This was Wolverine's schtick for many years; that he couldn't remember his Dark and Troubled Past , yet kept running into people that were from it. House of M cleared this and had him remember everything, which lead to the discovery of his son Daken.
XIII.

Fan Works

This Trope pretty much describes "Ben", the protagonist of Shadowchasers: Torment. He wakes up in a morgue, and has no idea where he is, but his memories return to him in bits and pieces as the plot progresses. As a Walking Spoiler, he's difficult to describe.

Film

Jason Bourne embodies this trope perfectly.

Literature

Jason and Percy in the Percy Jackson & the Olympians Sequel Series The Heroes of Olympus.
Rachel is this in the first Megamorphs book of Animorphs.
Touma in A Certain Magical Index doesn't begin the series with amnesia, but he loses all his memories at the end of the first volume. He never regains his memory, and has to hide his amnesia from others. It's later revealed that he did have a specific form of amnesia when the series began, which makes him unable to remember or form new memories of one particular character.

Live Action TV

Kamen Rider so far had three heroes with Amnesia:
- Tsugami Shoichi, aka Kamen Rider Agito
- Kadoya Tsukasa, aka Kamen Rider Decade
- And Phillip, aka one half of Kamen Rider Double
This trope, along with his knowing everything, was the premise for the short-lived series John Doe.
Data becomes this in the Star Trek: The Next Generation episode "Thine Own Self", where crashing on a planet during an away mission damages him and causes him to lose his memory, not even aware that he is an android. His morality program is still working, though, and he is able to save a town from dying of radiation poisoning.

Video Games

Slayn Wilder, the protagonist of Growlanser: Dual Darkness begins the game with amnesia.
In Neko Kawaigari, the player is a dog-man named Jack who, you guessed it, has amnesia. He's rescued by the head of a clinic for catgirls. In order to repay her, he becomes an odd-job man at the clinic, helping with the patients.
Pokémon Mystery Dungeon: Excepting the Japan-only Wii Ware games, the player is a Pokemon that was once human and lost their memory. However, unlike a normal Amnesiac Hero, they have to slowly learn fighting skills just like any other Pokémon instead of having them naturally. In the first set of games, this was self-inflicted.
This has almost become a Running Gag in Rune Factory games, with one character in Rune Factory 3 saying that "amnesiacs are a dime a dozen around these parts." The only protagonists so far not to be amnesiacs are Aden and Sonja, perhaps because Sharing a Body would be too awkward for two people who hadn't known each other for quite some time.
The Nameless One from Planescape: Torment, except he (obviously) doesn't remember his own name (his name is the last thing he remembers). Oh, and the soon-to-be sidekick who finds him is a floating talking skull who didn't so much 'find' him as was waiting for him to wake up again.
Daniel from Amnesia: The Dark Descent with a twist; he induced it himself so he wouldn't remember the horrible things he did.
Galuf from Final Fantasy V.
Raz from Overblood.
The Fateless One from Kingdoms of Amalur: Reckoning. Probably due to dying and coming back to life. Hell, the body s/he's in isn't even his/er original.
Revan from Knights of the Old Republic.
This is the premise of the action/adventure game BioForge.
Cave Story begins with protagonist waking up in a cave with no memories. It takes exposition from other characters to learn about his true identity.
XIII.
Booker, the hero in BioShock Infinite. A glitch in the Portal Network that takes him to Columbia causes him to forget who he is and why he came there, other than the general idea that he's on a rescue mission, and doesn't figure it out until he finds who he is supposed to rescue - Elizabeth - and she explains it to him.

Web Comics

Trace of Twokinds is this. We've been told some choice details of his past, and his current goals are so drastically different from his old ones that the world may be better off if he stays this way.
The Hero of RPG World is also amnesiac, such that he doesn't even remember his own name (Everyone Calls Him Hero).

Web Original

Mei, one of the members of the Fellowship in The Questport Chronicles.

Western Animation

The Hollow is a Netflix original series that is this Trope. In the first episode, the three protagonists - Adam, Mira, and Kai - wake up in an underground bunker, with no memories, only discovering their names due to notes in their pockets. After escaping, they discover they have super-powers, and are roped into fighting mythology-themed demons, and along the way, try to figure out who they are.
In the aptly-named Code Lyoko episode "Amnesia", Ulrich becomes this, for that episode only. He gets infected with nanobots created by XANA that give him amnesia. He initially doesn't remember anything, but starts to get flashes of memories later on (specifically of his friendship with Odd, his romantic feelings for Yumi, and his Lyoko duties). He even ditches Sissi (who was taking advantage of him) to find out where his mind was telling him to go as he slowly remembers Lyoko and his duty to "do something important".