Bat-Mite is an imp similar to the Superman villain Mr. Mxyzptlk. Appearing as a small childlike man in an ill-fitting costume, Bat-Mite possesses near-infinite magical powers and comes from another dimension, much like Mr. Mxyzptlk. Bat-Mite idolizes Batman, and thus he has visited Batman on various occasions, often setting up strange events so that he could see his hero in action. Bat-Mite is more of a nuisance than a supervillain, and often leaves his hero alone when he realizes he has angered his idol. Bat-Mite thankfully has never appeared in live action.
Bat-Mite regularly appeared in Batman, Detective Comics, and World's Finest Comics for five years. Bat-Mite and Mr. Mxyzptlk teamed up four times in the pages of World's Finest Comics to plague Superman and Batman together, as well. However in 1964, when the Batman titles were revamped Bat-Mite vanished along with the other extraneous members of the Batman family such as Ace the Bat-Hound. After this, only three more Bat-Mite stories were published in the pre-Crisis DC Universe.
Bat-Mite made an appearance in the series Legends of the Dark Knight, although he may have been the hallucination of a drug-addled criminal named Bob Overdog. This version of Bat-Mite later appeared in Mitefall, a one-shot book which was a parody of the "Knightfall" Batman storyline.
In the post-Crisis issue Superman/Batman #25, it was revealed that the Joker had gained Bat-Mite's powers by absorbing his essence; at the end, Bizarro was able to free him. As such Bat-Mite has been fully re-established into the current continuity, though his exact connection or whether he idolizes Batman like he previously did, has not been established.