For hardcore multiplayer FPS, Quake Live/Quake 3 CPMA (VQ3 ruleset) is the unequaled standard because of:
* Its extremely balanced and select arsenal (each weapon has a situation where it shines, which don't overlap much), especially in CPMA where the RL and RG damages were exchanged in order to favour predictive instead of hitscan weaponry.
* The very thoughtful level design that exploits the 3D dimension and special Quake movements while balancing very well the positional advantage/risk of powerup areas. The use of very distinctive and far reaching item pickup or terrain (e.g. jumper or water) sounds also helps tying this together.
* The movement speed of these specific variants hits peak balance, where it's not as boring and slow as vanilla while maximizing the importance of positioning; as opposed to CPM where you roleplay as a Trackmania player with guns.
* Like most older Id games, open sourced so you have very good source ports (ioquake3, quake3e, cnq3) that run on everything and with modern technology (e.g. Vulkan). That's also how you get an incredible amount and quality of user content like
https://www.lvlworld.com/,
https://www.doomworld.com/idgames/ or
https://forum.zdoom.org/
* Minimalism is the norm. Weapons are color coded to help fast identification and a lot of people play with flat mipmaps and/or fluorescent green Keel/pm models.
* It's one of the best spectator sports: when you watch someone like Rapha play 1v1 at an important competition, it's like watching a shogi and boxing match all-in-one.
* While not as good as UT on the out-of-the-box availability of different gameplays, we now have some incredibly fun stuff such as FreezeTag (my favourite), Instagib, DeFRag or Rocket Arena.
* Arena FPSes prevents the use of long camping; can't control the map by staying static.
Here's a video that should make people want to know more about it:
Some other very good multiplayer FPS are Quake 4, UT2k4, Enemy Territory, Warsow (basically CPMA in gameplay) and supposedly Shootmania.
For other games, I'll just list some I consider classics that everybody who can appreciate quality should play:
* FPS: Doom 1, 2 and 3 (including the
incredible community content, cf Cacowards), Blood, Duke Nukem 3D, Rise of the Triad, Shadow Warriow, Tribes: Ascend, Return to Castle Wolfenstein
* Platformer: Castlevania (in order of "bestness": Symphony of the Night, Aria of Sorrow, Rondo of Blood, Harmony of Dissonance )
* RPG: Golden Sun I & II, Diablo 2/most Disgaeas (caution: very grindy), Final Fantasy (especially the Tactics sub-serie), Etrian Odyssey, Pokémon up to the 3rd gen (2nd is best), Tales of Eternia, Tactics Ogre: Let Us Cling Together, most SNES Fire Emblem titles, Breath of Fire (up to IV), SaGa Frontier 2, Star Ocean serie, Suikoden II, Xenogears, Chrono Trigger, Secret of Mana, Sakura Wars I & II, System Shock serie
* Others: Dwarf Fortress, (Z)Angband/Nethack/Crawl for roguelikes
Sadly, I don't have a lot of experience in some styles like racing games (I've heard that pro racing sims like rFactor 2 are incredibly fun) or RTS (Warcraft III, Age of Empire 2, Starcraft 2 and Warzone 2100 are supposedly classics).