Valheim

Can vouch for Deep Rock Galactic, Ember Knights, Ultimate Chicken Horse, and Factorio

Edit: Pulsar: Lost Colony is also good, but you'll need to have two bots as well

Left4Dead2 can be played by 1-4 players. Empty player slots are filled by AI bots.

Lovers in a Dangerous Spacetime is fantastic.

Elden Ring is a great one, especially with the Seamless Co-op Mod. Besides that, my friends and I used to play Borderlands 2 and Outriders.

Astroneer, Raft, and if you like mindless indie stuff Generation Zero.

Remnant 1 & 2 if you like souls type third person shooters.

Dungeon of the Endless and the new version Endless Dungeon.

Unsorted, quick and probably incomplete list of my personal favourites:

• Helldivers
• Nine Parchments
• Overcooked! 2
• Sonic & All-Stars Racing Transformed Collection
• Gauntlet™ Slayer Edition
• Lovers in a Dangerous Spacetime
• Sacred Citadel
• SpeedRunners

Ever heard of the Trine series? 5 games by now (can only speak about the first 4 though), and they are really fun together. Basically 2d puzzle games with 3 different characters that all have their own abilities, which leads to many different ways to solve puzzles. Highly recommended.

I haven't seen it mentioned, but Minecraft is also multiplayer.

Unreal Tournament 2004, with few players it turns its normal frantic and fast paced gameplay into a suspensfull slower experience which is awesome.

I think you can get it on the internet archive as it stopped being sold on gog and steam this spring.

OpenRA - Do you remember the old classic series Command & Conquer ?

OpenRA takes the old original game, updates the controls to modern RTS controls, add new ai to play against, add support for modern resolutions and adds a good internet multiplayer system, all of this for free!

OpenRA can be downloaded att https://openra.net

For the king. Made for 3 people

Remnant 1 and 2 are both 3 players

Nobody mentioned the finals. Free to play fps competitive shooter with teams of 3. It's been crazy addictive for my friends and I. If you like fast paced hectic fps games it's loads of fun.

Trine 2! It’s a side-scrolling action/puzzle platformer, and a rare game actually made for 3.

Sea of Thieves

Elden Ring with the seamless COOP mod has been very fun for my two friends and me. The experience isn’t 100% perfect (some bugs) but exploring the Lands Between with buddies and fighting the bosses together has easily been in my top 3 COOP experiences up until now.

Deep Rock Galactic!

I'm in a poly throuple and we play these games:

-League of Legends

-Super Mecha Champions (It's like Apex but with bots and the real players aren't as good so we don't get absolutely crushed every time we play which is nice)

-Stardew Valley

-Eternal Return (League + Battle Royale)

-Divinity 2

-Overcooked

-Borderlands

-FF14

-Tabletop Simulator (Board Games)

Online or offline multi-player?

As for couch coop Rayman Origins and Rayman Legends is some of the most fun I ever had with friends gaming.

I didn't see anyone mention Stardew Valley. My two kids and I put in 100+ hours on our farm. It became a nice, zen, pre-bedtime ritual.

If you have VR headsets, Walkabout Mini-Golf is surprisingly fun. In fact, I'd argue that it only becomes fun with 3 people.

Some of my favorites for 3 are the same for 4.

Streets of Rogue and Vagante are challenging roguelikes that scale effortlessly for co-op of various numbers of players. There's also Mercenary Kings, which I admit I enjoyed more than most, but it's like the cross section of Mega Man action with Monster Hunter structure. Much more recently, Baldur's Gate 3 probably hits its sweet spot at 3 human players, since you want to have an NPC slot around in your party of 4 for the story quests that are relevant to that NPC.

Nine Parchments and Magicka 2.

Edit: also, the Trine games. And on PlayStation we enjoyed Diablo III and Alienation, both of those are three player as well.

If y’all have PS3, Lord of the Rings: War in the North. Specifically a 3 player co-op game. Like actually 3 player, not 4 player where you don’t need a 4th. I enjoyed it and have good memories playing with friends, it’s really fun and silly and the servers are still up.

Civilisation V

If you're into RPGs, both Solasta: Crown of the Magister and Balgur's Gate 3 are great coop experiences.

Monster Hunter

PlateUp! has completely consumed a couple of lan parties. Awesome Roguelite restaurant game.

I mean, love it or hate it, Destiny 2 is literally made to be played by (mostly) 3-person teams. I’ve had a boatload of fun with it over the years.

Some beat them up: tmnt, streets of rage 4

Also since you did not mention playing remotely or not (although there are ways around that: parsec, steam remote play together...) almost any couch coop game: overcooked, moving out, unrailed...

Edit: all of those I cited have a online multiplayer mode I think, for overcooked the AYCE edition contains all of the first edition content but brings online MP amongst other things

I play with 2 of my brother in laws. These are my favorites:

Elden Ring

Dark Souls 3

Borderlands 3

Ghost of Tsushima

Rocket League

Avengers

Remnant

A couple older games:

Supreme Commander: Forged Alliance. A very complex RTS with a pretty steep learning curve and advanced strategy. Awesome game but not casual.

Alien vs predator games are specifically 3 player (marine, alien , predator). Not sure if there is a modern version. Interesting because each of the 3 play differently.

My wife, my brother, and I like to play Hunt: Showdown.

Towerfall

Boomerang Fu

Hammerwatch

Splitgate

Quake Live / Champions

Stellaris allows many players if you like those types of games. Only the host needs dlc if you want to pool your cash and buy some. But yeah it can be expensive.

Honestly playing a lot of The Finals recently

1-3 players, team based, capture the flag like, free to play, your team vs 2-3 other teams, fast paced