The vast majority of contemporary games offer subtitles for in-game dialogue, but make no attempt to provide full captioning for other important sound cues. Sound effects, which are vital to a full understanding of the gamespace (as opposed to the representational space of the game), are needed in order to alert deaf players -- or even players who choose to play with the sound off, such as commuters playing on a handheld device without headphones.
Note that closed captioning might not be the best solution for certain audio cues, specifically vital cues that occur very regularly. Visual effects that represent the audio cues in question obviously provide the same support for deaf players as well as players of standard hearing, and are usually inexpensive to implement.
Half-Life 2 includes full closed captioning, and is considered a pioneer case. Doom 3 has been modded by its technical community to provide a closed captioning function. The mod is called Doom[CC] and the project was lead by Reid Kimball, a hearing-impaired gamer and game developer.