Tulpa

A tulpa is an imaginary friend-like entity created by a character that differs from other imaginary friends in the fact that the character can actually see and hear it.

If the character must actively concentrate to keep the entity there, then it's an Imaginary Friend.

Anime & Manga

 * In Soul Eater, the titular Soul Eater turns out to be a tulpa of Kyousuke Tanaka. It is also heavily implied that the ENTIRE SHOW is a tulpa in the mind of the viewer.

Comics

 * An alternative and fantastical origin story for Doctor Doom had Mr. Fantastic create him as one of these.
 * It is possible that Hobbes from Calvin and Hobbes may be a tulpa.

Films -- Animation

 * In Ratatouille, Remy creates a miniature version of chef Gusteau.

Live Action TV

 * In Supernatural, The heroes are investigating a haunted house and realize that a Tulpa is to blame when they see a tibetan sigil on the wall.
 * The titular character in Out Of Jimmy's Head has several.

Real Life

 * Several people on the reliable internet have claimed to have created some, with beliefs ranging from "It's magical" to "It's a self-induced schizophrenia".