Hearthstone or just about anything Blizzard made
From secret cow levels to pop culture references, Blizzard has been sneaking in bits of humor, with varying levels of blatancy, into its games for years. Blizzard's free-to-play card game Hearthstone is certainly no different. Cards come into play with silly voices and one-liners, some cards are even references to jokes themselves and the flavor text is dripping with sarcasm and jokes. In many ways the lighter tone helps to smooth over any incongruity between having, say, gnomes with silly voices and various demons being summoned to play side by side.
Monkey Island series
No list of funny games would be complete without some of Lucasarts' adventure game heyday. While you could make some strong arguments for Sam & Max, Full Throttle or Day of the Tentacle, it's the misadventures of Guybrush Threepwood that we remember most fondly. With legendary game designers like Dave Grossman, Tim Schafer and Ron Gilbert at the wheel, the Monkey Island series is endlessly entertaining with it's subversion of other adventure games, typical heroic characters and pirate themes. A rubber chicken with a pulley in the middle or insult sword-fighting are classic gags that every gamer should know.
A fair number of the titles we've discussed so far have weighted more towards the silly and zany end of humor. Portal is perhaps gaming's best example of a dark comedy. Most of the game's humor comes from GLaDOS, voiced by Ellen McLain. Spoilers: GLaDOS is a crazy murderous AI, but it's her flat and dry messages and directions that really sold and pushed Portal into being more than just a clever puzzler. Ardent fans will quickly spot their favorite lines about cake or Weighted Companion Cubes, but personally I enjoy the antics of the little voices added to the automated turrets.