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 Mysterious 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.

Film

Jason Bourne embodies this trope perfectly.

Literature

Jason and Percy in the Percy Jackson and The Olympians Sequel Series The Heroes of Olympus.
Rachel is this in the first Megamorphs book of Animorphs.

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.

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.

Web Comics

Trace of Two Kinds 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.