Here's some of my friend group's favorites with old and new games mixed in, we go all over the place!

RTS

• Beyond All Reason - If you're a fan of Total Annihilation, Supreme Commander or Planetary Annihilation, or if you like RTSs and want to be in control of tons of units on huge maps check this out! It's Open Source and free.
• War40k Dawn of War - One of our favorite RTS's, the mix of unit loadouts and varied factions is amazing! Make sure to get the FoV and Widescreen mods here.
• Command and Conquer: Tiberian Sun - Classic RTS, Now free through cncnet. Subterranean APC Detected!
• Age of Empires 2 - Classic, Wololo
• Gates of Hell: Ostfront - Really underrated RTS, the sound design, ballistics, attention to detail and variety of units is awesome. Allows direct control of infantry and vehicles, has a inventory system, you can steal weapons off vehicles, repair etc.

FPS

• Half-Life (GoldSrc Engine) Deathmatch - Classic DM game with fun weapons, The tension on the crossfire map after the button is pressed inside the bunker is amazing. Tons of mods available for it such as: The Specialists, Zombie Panic, Pirates, Vikings and Knights, Science and Industry and more! Oh my god, we're doomed!
• Half-Life 2 (Source Engine) Deathmatch - Throw toilets at each other's heads with the grav gun! There's tons of mods!
• Garry's Mod - The Deathrun game mode specifically, Most extreme challenge with a cruel twist, one friend will be picked per round to set off traps and environmental changes as everyone else tries to get through an obstacle course of death.
• Titanfall 2 - One of the best twitch FPSs since Tribes, CS, HLDM, Quake II, and UT. The movement is incredible and gunplay amazing. Try the Northstar client if the official servers are under attack or you want more variety with mods.
• Natural Selection 2 - Really good blend of FPS and RTS elements, 1 player on each side is a commander and choose upgrades, where to build, drop supplies, give orders etc. Aliens vs Marines with strategic depth. Can be a steep learning curve for some.
• Arma 3: SOG Prairie Fire DLC - One of the best Arma DLC's out, lots of free updates have happened, If you like Vietnam era vehicles and infantry and co-op with friends it's great. You'll need a group of friends to play. If you want something more modern in both theme, game engine and quality of life, wait for Arma 4.
• Alien Vs Predator 2 - Face hug your friends, catch them in the Predator's net, Enjoy that classic Pulse rifle sound and screaming ! Any servers still surviving likely won't be populated depending on the time of day. I don't know where to buy this officially anymore, there must be some kind of rights issue going on for re-releasing it. Game Over, Man! Game Over!

TPS

• Risk of Rain 2 - ALL THE ENEMIES EVERYWHERE
• Red Faction 2 - The building Destruction in this is really fun! Hitting friends with a giant hammer is satisfying too. There's a remastered version out but I've never tried it.

Strategy

• Total War: WARHAMMER III - The Immortal Empires mode is really fun, warning though, there's a lot of DLCs, your favorite army or one you're interested in might be locked behind one.

VR

• Pavlov VR - Awesome FPS, semi-realistic firearm operation with mod support!
• Phasmophobia - Ever wanted to feel what it'd be a paranormal inspector, possibly scoping a place out to validate if the Real Ghostbusters should arrive or not?
• Forewarned - A unique take on the Phasmophobia type game, Egyptian tomb themed, if you die you can come back as a good mummy to help friends or bad mummy to annoy friends!
• VTOL VR - Semi-Sim Flight, Co-op, You can actually reach out and flip console controls / switches! It has VTOL, Jet and Helicopter vehicles.
• Iron Wolf VR - Really amazing WWII Submarine co-op game, I really wish development could have continued but one of the lead developers has unfortunately passed away who was the best friend of the other dev. Tragic but they left behind something awesome for people to enjoy.

2D Mayhem

• Duck Game - Pure madness, a 2D Shooter with Ducks, Crazy weaponry from a mind control gadget to a simple banana. Great online and even better if you can all get together in the same room to see everyone's reactions. Quack!

The following three games are meant for local / couch gameplay, but using steam remote play or parsec works.

• Crawl - Really cool, it's a dungeon crawler except only one player is a human, the others are monsters. If a player monster kills the human, they take their place. The final boss's body is controlled by the monster players! You can choose a deity and set of monsters you might spawn as and upgrade them as you play and become more powerful.
• Towerfall Ascension - 2D Archery combat game, really intense short matches, the mechanics are straightforward but hard to master.
• Hidden in Plain site - Fun little party game, you try to blend in with a crowd of NPCs to achieve your goal or avoid being eliminated by other players.

I hope someone finds something new in this list, or perhaps some good memories.