Portal and Portal 2!

The Monkey Island games come to mind. A Bard's Tale maybe?

People (not me), seemed to really like Thank Goodness You're Here. Undertale is a popular one. Date Everything seemed funny from what I saw of it, and if playing with friends things like peak, baby steps, or getting over it. Lots of different genres there, but steam also has a tag for comedy games. Even if you don't end up buying it on steam, you can always check that out in case you don't get enough options via comments.

I dunno if it’s “comedy based” but I find Grim Fandango really funny.

If you're into some point and click, I might suggest the Sam and Max collection

South Park: The Stick of Truth and its sequel were really funny and the RPG gameplay was a lot more fun than I expected. I’ll also second the recommendation for the Monkey Island series.

Thank goodness you're here (already suggested and upvoted) and McPixel

Grim Fandango!

Never has a game made me laugh out loud like when I first discovered it. Clever humour, unique characters, and each line of dialogue is packed with effortless charm and wit. Not to mention the philosophical themes disguised as one man's quirky Day of the Dead -themed quest to get to the afterlife.

The puzzles are a product of its time so a walkthrough might be needed. But that's forgivable for the game's big picture.

Wish I could wipe my memory of it and play it all over again.

West of Loathing and Shadows over Loathing are two really funny and silly games.

I liked Guardians of the Galaxy

Deadpool the game is super funny if you can get it. There is no legal way to get it.

The original ace Attorney trilogy is pretty good with humor, some people enjoy the humor in the somnium files, yazuka zero's side content is pretty funny.

Unmetal is a fun spoof on Metal Gear/MGS games

The older Sam and Max games were great.

Played it over a decade ago but Jazzpunk remains very fond in my memory. Can highly recommend it

HITMAN! The core story/cutscenes form a very serious, grim premise. But, the actual gameplay, and the writing of the many dozens of NPCs in each level, is filled with humorous charm and tongue-in-cheek Bond-eque silliness. Characters will acknowledge 47's often paper-thin disguises, make silly remarks about excuses to take off early, or alluding to how horrible it would be if some freak accident occurred. Plus, the mechanics can involve things like dropping banana peels for people to slip on, or luring people with a cartoony explosive rubber duck.

It takes a bit of time to get used to how the game wants you to explore, and stop trying to brute-force it like a stealth game. Quite often, some of the main intended ways of going about a mission involve little to no stealth. It's a lot of fun and very replayable.

Depending on when you were born: Class of '09

I'm not sure how it would hit for non-millenials but if you went to school in the early aughts the entire series is great.

High on Life is full of jokes from beginning to end. There is a surprising amount of detail and commitment to most of the jokes. It's a shame about Justin Roiland though.

Pizza Tower

The Looker is a short parody of The Witness and it’s free on steam

Both MediEvil games on PS1. Yes they're kind of dated now, but I'll always have a soft spot for Sir Daniel Fortesque and his skeleton slapstick.

Battleblock theater

Have you got the deluxe edition of Stanley parable? It really got me laughing how much it jokes about sequels.

Tales from the borderlands is one of the funniest games I've ever played. It's a telltale game.

West of loathing is a turn based game but it's too unserious with lots of jokes.

South park: The stick of truth is probably the best comedy game I've ever played. You can also try the sequels.

There was an old deadpool game but I can't remember the name. If you know deadpool, you can expect the type of humour in it. Might not have aged well though.

And if you want a great game with comedy, the YAKUZA series is in a class of it's own. One minute you'll be laughing your ass out, and the next minute you'll be bawling. I'd recommend not to start with yakuza 0. It's a prequel but the story is so phenomenal that, after playing, other parts feels average in comparison.

Esoteric Ebb

It's Disco Elysium, but you're a cleric in D&D in a nutshell.

Baby Steps

There Is No Game. It's not very funny, but still pretty funny.

It's rather dry humor but I had a pretty good amount of laughs and chuckles from "Thomas Was Alone"

If you're enjoying The Stanley Parable, you'll probably like Do Not Press The Button To Destroy The Multiverse.

"There is no game"

Promise Mascot Agency had some really solid writing.

Dinocop. There's a demo on steam

Just say not!

Sir Whoopass was pretty fun for what I played, and absolutely delightfully funny the entire time

Crashlands.

• Nelly Cootalot: The Fowl Fleet (written by British comedian Alasdair Beckett-King who is occasionally on the telly)
• Yorkshire Gubbins

I think there's free "prequels" or other ones from both series, if you wanted to test your reaction to the humour.

Mitchmanix has a whole channel playing through comedy games.

One of my personal favourites is The Deadly Tower of Monsters.

I haven't got very far into it, but Rustler is a pretty funny top down view GTA spoof.

Ink Inside.

Made by ex Cartoon Network + horror devs. Game is basically a cartoon show you play. But with unique combat, a funny narrative, and game mechanics that often can make you laugh with how silly it is (if you like slapstick)

It's two player co-op as well, with some killer VO.

Brian David Gilbert is one of the leads, so if their humor works for you, you should check it out! 😁

The Dragon Quest series has lots of comedic moments and dialogue, but its a very specific brand of a bit antiquated japanese humor that falls flat for some people.
Xenoblade 2 as well, especially in the cutscenes, and the dialogue delivered by the cutesey mascot "Nopon" race characters.

KIngdom of Loathing

Super Bunny Man and Heave Ho for multiplayer games. Single player is doable, but multiplayer is where the laughter really hits.

A little older, but Bard's tale cracked me up pretty good when I first played it.

Good joke games are rare.

If you like narrative games I would recommend "Dr. Langeskov, The Tiger, and The Terribly Cursed Emerald: A Whirlwind Heist". It is very short (15 minutes), but it is good, and it is free: https://store.steampowered.com/app/409160

Another silly game with lots of jokes in it is "Kraken Academy!!": https://store.steampowered.com/app/1158220