For me it's probably Jazzpunk, but I liked Disco Elysium too. I've been looking for something to scratch that "Jazzpunk surrealist comedy itch" for a while and not many games have come even close.
For a game that's a full comedy romp, West of Loathing consistently ruined me with laughter. The spittoon descriptions are probably the most derangedly funny writing ever put into the world. I've got to remember to play the sequel one of these days. Its also extremely mechanically satisfying, with several enticing roleplaying moments (as well as the occasional dramatic or scary moment that hits just as well as the comedy)
For a game that's not explicitly only comedy but still hits strong marks, Yakuza 0 is a full meal. While most Yak games are fairly wacky when it comes to sidequesting (1 being perphaps the single exception, as the beginning of the series was quite dry), 0 feels like the one where they really hit their stride. There's so many flat out ridiculous moments (you've most likely seen the chicken, and that's just one of many) that you even forget this is also a heavily dramatic story and a full blown action beat'em up.
One game series that is not known for being especially humorous actually can be: The Halo games. More specifically the enemy grunts. If you sneak up on them and listen to their dialogue, their mix of faux bravado, cowardice and delusion of grandeur can be really funny. Especially because Master Chief is “The Demon” to them. A near-mythical monster. Just choosing the right time to reveal your presence to the grunts can result in comedy gold.
Stanley Parable and Trover Saves the Universe are both pretty funny. I'm sure there are a ton of really funny games, but for some reason, they're not coming to mind.
The game I've laughed the most while playing is Jackbox. Fibbage and Quiplash have me in stitches every time, although it depends on how funny your friends are.
For me its gotta be Donut County. I was baked out of my mind and my best friend was like "Dude you gotta play this game" and handed me his controller. It was awesome.
Ultimate Chicken Horse might be one of the top party games for getting a laugh for me. It's always fun to see someone hyperfocused to make a jump, only to get hit by an arrow, followed by a wrecking ball hitting them into a sawblade.
Not single player/story funny, but I don't think I've absolutely lost it to any game (possibly even any thing) more than Gang Beasts. Get 8 friends together for a rumble and cry laughs will be had.
One time back when we were living in an apartment with an inward courtyard facing window, my wife and I were laughing so hard a neighbour threw something at our window to get our attention so they could shout at us to keep it down. It was only 10pm on a Saturday :/
Some coop games, like Battleblock Theater or Magicka, were definitely the most funny for me, with all the dumb stuff you can do, fuck with your friends, etc. but those depend on the people you play with. With friends, every game can become super funny though, even more serious stuff.
As for single player, the ones I remember the most were Donut County and maybe the Frog Detective games, those had some really funny moments and writing.
First off, Rare had a reputation for good games, but they were cute, child friendly games. Conker was even a cute character with child friendly games. Then they made this... thing, which starts with Conker hungover from a night drinking and quickly descends into him fighting a giant poo monster. The game was rated R/18, which was crazy for Nintendo. The amount of little movie references everywhere was insane, also.
Callahan's Crosstime Saloon - (it is now abandonware, you can play it for free) if you have never heard if it but like sierra/lucasarts style games you really should give it a try. Extremely funny.
But also the Monkey Island Series and Grim Fandango?
Any shovelware with lots of bugs, continuity errors, and English language fails. I’m the type of person who believes in “so bad, it’s good” (or at least so bad, it’s funny). Warning for TVTropes link.
Hatoful Boyfriend has some really great moments, especially if you pursue Anghel or Okosan. It also will make you cry your eyes out in the true ending, so there's a good balance.
Just recently played A Hat in Time. We're never told, but every detail points at this being the fantasy adventures of a little girl with A LOT in common with Calvin from Calvin and Hobbes, an overabundance of imagination and hyperactivity. Charming and funny (well, save for Queen Vanessa, which I feel was instead a masterpiece in ambience). Loved it, gotta try the DLC. Just be ready for hard platforming at many places.
Someone else mentioned Procession to Calvary - an adventure game set in a cut and paste world of renaissance art with a very surreal plot and sense of humour. Pythonesque.
There Is No Game is pretty hilarious, the voice acting always makes me crack up.
Agatha Knife is a funny point and click adventure game where you're a 7 year old girl who's a butcher and needs to set up her own religion sacrificing pigs in the basement for... Reasons.
It's not a very good game, but I laughed my ass off through the Deadpool game. The one that immediately comes to mind though is Bulletstorm. It definitely set the bar for high-brow, sophisticated humor.It's a shame that People Can Fly chose to go with Outriders, because I'd kill for Bulletstorm 2.
Disco Elysium is the most recent game that was just chock full of humor, though maybe not focused on it specifically... beyond that the only games I can even really think of that had a focus on comedy were the old LucasArts classics. Sam & Max, Full Throttle, Monkey Island... And Borderlands.
I was just thinking about how this doesn't seem to be a thing anymore. Where are the comedic oriented games? Why is everything so damn dark, and serious and brooding nowadays?
But I haven't played that Not-Really-Rick-and-Morty-shooter. I heard that was funny.