Great choice by everyone like the Mario RPGs including Paper Mario series and the Mario Luigi Games, the wario ware games, conkers bad furs day, worms, grimm fandango, the monkey island games, and others, I would add the Ace attorney series, they have lots of serious themes and mature situations but also tons of double entendre, snarky and humoruous dialogues, despite being signaled for things like the localization I always thought they did a magnificent work and they are really funny.

Conkers bad fur day

Ratchet and clank up your arsenal and the other PS2 Ratchet games.

The GTA games

Stupid Invaders. Old as hell now, but I absolutely had a ball with this game back in the 90s.

Elite Beat Agents, Banjo Kazooie, and the Mario&Luigi series were all hilarious, but the funniest game I ever played was 'Harvey Birdman: Attorney at Law'.
https://en.wikipedia.org/wiki/Harvey_Birdman%3A_Attorney_at_Law_(video_game)
Designed by Capcom in the same style of Ace Attorney, but with jokes and writing equal to the TV show it was based on.

I can't think of a ton of games that legit make me chuckle. And it's not like I'm tough to please or don't have a sense of humor, as I laugh my ass off at plenty of comedy films and TV shows. More often than not, I feel like games that try to be funny come off as trying too hard, to the point where they miss the mark or fall flat. The humor is often juvenile, simple, and not particularly clever.

There are a few that stand out though, which at least have funny moments in them -

- South Park: Stick of Truth and Fractured But Whole would probably be at the top of my short list.
- Borderlands 2 is also full of some zany humor, doesn't always hit, but Handsome Jack and Tiny Tina both have some hilarious moments, Clap Trap has a few.
- Maybe Conker's Bad Fur Day at times. Though I will say most of the humor there came from the Great Mighty Poo and his theatrical song. 
- Castle Crashers has a few silly moments, like the level where you propel across the level by way of crapping deer.
- Sort of a separate entity in terms of type of humor, but I was laughing my ass off at the ragdoll physics of Human Fall Flat, especially when playing with a couple dozen other people all flailing and fumbling around.
- Some Jackbox Party Pack content, mostly Quiplash. Credit to the silly answers of people I've played with moreso than the game itself though. Fun fact here - my uncle voices the Quiplash host Schmitty XD. He's a pretty cool (and funny) dude, and it comes across in the game.
- Oh - and the radio in GTA4 was good for some yuks (still haven't played GTA5) 

Lego City Undercover. That game was hilarious!

The one that made me laugh the most would be South Park: The Stick of Truth, it's like a big South Park episode and it's packed with funny moments (my favorite being the Nazi Zombie Fetuses). Runner up would be Portal 2, where GLaDOS and Wheatley are hilarious.