In recent gaming, Gears of War has some...
and the Oddworld franchise too.
but back in the old days... I remember playing a Nintendo 64 game with a crisp sense of humor:
Mystical Ninja: Starring Goemon!!!
Very original game!
A lot of WTF moments!!!
Taken from Wikipedia:
"Humor
The story of Mystical Ninja Starring Goemon, a quest to thwart dancers in a peach-shaped spaceship from using laser weaponry to convert Japan to a giant stage and its citizens to loyal dancers, is steeped in surrealist and Japanese humor. Many reviewers and writers smirked at Konami's plot summary and story details.[5][14][15] The plot's sanity is further broken down by the Goemon series' use of anachronistic technology and references, including giant robots, airplanes, and pizza.[16] The game's dialogue is peppered with horrible jokes, offbeat humor, and a few instances of sexual innuendo, such as Mokubei's admonition to wield his pipe to impress young girls. In the Japanese game, Wise Man collected hentai magazines and pornographic posters rather than automotive publications.[17] A laugh track punctuates certain jokes. A [kuː] sound sometimes concludes awful puns.[18] The game often breaks the fourth wall by textually parodying certain game conventions—such as an non-player character's tendency to be fixed in one position."
