The most popular Batman games in the Lego DC Comics Super Heroes product line are Lego Batman: The Video Game, Lego Batman 2: DC Super Heroes, and Lego Batman 3: Beyond Gotham.
These games are developed for use on the gaming systems Xbox 360, Playstation 3, the Wii and the PC. All of these games are rated E for everyone for cartoon violence.
If you are looking for online games to play at no cost, the Lego DC Super Heroes product page has free games on their website for Batman as well. These games include Batman Demolition Derby and Batman.