I'm sure all of these have been brought up previously, but I can't be bothered to check. There are many types of games which contain comedic elements as a major factor. These are my favorites that aren't adventure games. Or Valve products:
1. Silly sports games. Your "NFL Blitz"es, "NBA Jam"s, "Mutant League Football"s, et al. These are (at their best) decent sports simulators (with simplified controls and/or more limited options than your standard EA Sports fare) that are packaged as cartoony, over-the-top expansions on the basic premises of the sport. I'd also include "You Don't Know Jack" in this category. Because I feel like it.
2. Games that let Japanese comedy do its thing to such an extreme that it's glorious. Far too many to name all of them, so I will name some of my favorites with brief taglines: "Katamari Damacy": The Joy Of Scale; "Odama"; Finally The Pinball Game You've Been Waiting For, The Pinball Kills People!; "Killer7": Conventions Are For Suckers; "Chibi-Robo": Sweeping Counts As Gameplay, Right?; "Cho Aniki": Well that's...
3. Reasonably Competent Spoofs. I am a fan of "The Bard's Tale" for Xbox and it genuinely evoked laughs, because a) Cary Elwes is a badass, and b) it picks its moments. As a fantasy RPG-ish actiony kinda game, I find it completely competent. None of it is the best in its field, but it all works together nicely. Why it works is that it routinely doles out the funny bits while avoiding the traps of too-oft-repeated quips, which makes it quite enjoyable. It has pretty good jokes that are set-up well from cut-scene to cutscene and running gags that usually work. Plus it also has one of the best "moral choice" systems, in that it doesn't change the story (just the weapons and skills you get) and instead of "good/evil," the options are "nice/snarky." Much better, at least for this setting. This category also includes "Evil Dead: A Fistful Of Boomstick"
4. Finally, standing (unsteadily) alone is "Stubbs The Zombie In: Rebel Without A Pulse." This bafflingly-unpopular gem is funny, more-or-less, from start to finish, and is the best action/comedy game I've encountered. I think this is because every element has such joy in its absurdity. Every attack, even just melee attacks is simple, fully controlled, and hilarious. Just getting Stubbs to run is enough to make me laugh every time. And man, it never gets old beating a cop to the edge of death with his partner's arm and then eating his brains; and even if it does, you can always just tell your zombie horde to do it while you're rocking around in your hover-truck. Every boss fight is different and creative, some using using the many different skills and weapons you've acquired and some entertainingly out of nowhere, and the story (which is entirely married with the gameplay) is well-developed, satirical, and... you know what? Fuck the rest of this post, I'm gonna go play "Stubbs" right fucking now!