Games don't always have to be serious. Actually, they do have potential for comedy and some games seem to exploit that quite well. Any games you find especially funny? Saints Row (most of them, especially The Third, and IV). References everywhere. It almost seems like everything in those games is a reference to something. If something isn't a reference, its probably a parody of a real life issue. The dialog can be quite amusing at times too. Serious Sam 3... the protagonist is hilarious at times, and at least once references an old TV ad while blowing something up. Grand Theft Auto V - Trevor... enough said.
Big Rigs Over The Road Racing. The game is extremely buggy and unfinished enough to be the most hilarious game ever made.
Saints Row 3rd must be one with best implementation of funny in games. Original Monkey island as well as Maniac Mansion were quite good with that too. Then in Just Cause 3 you can make lot of things that are funny, while game mostly attempts to be serious. Adventures of Nick and Willikins was pretty funny too, it is free point and click adventure game and incredible quality for a such.
Stick Fight: The Game is hilarious. A 2D fighting game with AK47s larger than the stickmen themselves and two-headed snowmen? The sense of humour is so offbeat that it's hard to take seriously.
Older fallout games (1,2, 3 NV) have some hilarious lines, some great references too, fo4 was good too, just not as funny.
Crashtastic, ten buck steam game that answers the question "What would happen if Mechano met Car Accidents?"
i would say My summer car, cubivore (obscure gamecube game, what did you expet from me?) and chibi robo zip lash. the last game isn't funny in itself, it's funny the fact that it ever existed.