Gregory House is often seen playing with his GameBoy Advance (beginning with the 3rd episode of the 1st season, Occam's Razor) and later Nintendo DS in earlier seasons of House. Often he is shown playing Metroid Prime Hunters, albeit with sound more fitting of a 1980's style game tracked over the more tepid Metroid music. In Season 2, he hands his GameBoy to a clinic patient while he talks to Wilson.
In Lines in the Sand, a severely autistic child gives House his PSP (Playstation Portable) as a gift for treating him, and after this we do not see House's GBA or NDS. However, the reoccurence of this newer handheld is minimal at best.
House likes video games as a whole, and is spotted playing a racing game on his PC in more then one episode. He loses when he looks away from the screen to berate his team.
In the season 5 pilot, Dying Changes Everything, House has also been shown to play an Xbox 360.
"What are you doing?"
"Level four."
~ Gregory House when asked by a clinic patient about his gaming.