Genre Refugee

A Genre Refugee is a Stock Character from some genre who appears in a story that is in no other way part of that genre. The character is probably Wrong Genre Savvy, or may be the cause of wrong genre savviness in others. Since genres often have different tones, the character may be a Knight of Cerebus or the inverse.

Anime

 * Rossiu from Gurren Lagann is a Real Robot character stuck in a Super Robot universe.
 * Gai Daigoji from Martian Successor Nadesico is the inverse: A Hot-Blooded Super Robot hero stuck in a Real Robot setting.
 * Kimi ni Todoke has three such characters, Chizuru, Ryu, and Kazuichi "Pin" Arai. Who seems to lost their way from a fiery shounen sport series to a lighthearted shoujo romance.

Film

 * The cowboy in The Big Lebowski. You could also make the argument that the Dude is a Stoner Flick side character who wandered into a Film Noir plot.
 * Tommy Frigo in Adventureland has wandered in from a raunchy teen movie.
 * Steve the Pirate in Dodgeball a True Underdog Story.

Literature

 * Quincey P. Morris from Dracula. Nothing like the presence of an American cowboy in a gothic horror story set in Britain to make you go "Say again?"

Live Action TV

 * The trio of mad scientist supervillains in Buffy the Vampire Slayer. After they disable the museum guards with an ice ray and steal a precious diamond, our heroes start searching the ancient tomes for a "frost monster that eats diamonds."
 * Gwen Raiden in Angel.

Video Games

 * In any other game Bang Shishigami might have been The Hero (and Dogged Nice Guy to Lichi). In BlazBlue he's treated with no respect, with his only canon "victory" to date being

Western Animation

 * An episode of Johnny Bravo involving all sorts of Halloween creatures also has a random gnome (of the lawn variety) mingling with them.