I don't know your console situation & my PC gaming stopped round the time of Hexen 2 & the original UT but I had enough time (I'm sad enough) to compose a list:
PSX - Dead Ball Zone (faster & angrier than Speedball, kick people in the nads until they PUKE!)
Saturn - Virtua Fighter 2 (no contest....but why would you have this console???)
PS2 - Dragonball Budokai Tenkachi (If you like your fighter games with a bit of meat)
OR
Soulcalibur 2 (If you like it fancy & flowing...just avoid Heihachi)
DreamCast - Soulcalibur (A crime you have to buy a console for this & Shenmue in an age of "Digital Downloads")
N64 - Personally the best multiplayer console EVER. You got Mario Partys, Lylat Wars/Starfox, Goldeneye, original Smash Bros, Jet Force Gemini, mario kart 64 & Diddy Kong Racing. All that!...and my top pick would still be WWF No Mercy...sacrilege I know.
GameCube - Smash Bros Melee (i know there are a lot more multis but i didn't have a huge GC collection)
Xbox - Dead or Alive 3 (didn't think I'd like it but I did)
PSP - Monster Hunter Freedom 2 (stupidly addictive if you know others with PSPs)
Xbox360 - Call of Duty 4 (steeper learning curve than Halo but better atmosphere & tighter maps)
XBLA - Worms or TMNT: Arcade with friends & Uno or Poker with strangers.
PS3 - If all your friends are virtual then Motorstorm (or wait for No. 2) otherwise I'd probably pick CoD4 again.
Wii - Resident Evil: Umbrella Chronicles (I <3 light gun games)
PC: Original Unreal Tournament. That was one of the happiest Summers of my life.
Most reccommended Rom for PC: If you have friends who don't mind cramping over the same keyboard I hold highly the fun of Mutant League Hockey.
If you have mad money & know where to spend it - Original Simpsons Arcade Machine...or maybe a Bram Stoker Dracula pinball machine but i love me pinball & that board was a mean mother...
Social games we don't need to mention cause you either love it or you hate it & they've been talked about to death - Guitar Hero.
On a personal note, this is the only time I will talk about/acknowledge Rock Band's existence. I'm sure it's a fine product & it looks to have strong DLC support. It's just that there is no love for Europe. There is no love for me. So therefore I have no love for Rock Band cause otherwise it'll break my heart as it flaunts it's wares to Canada but leaves me in the cold.One day it'll come & warm my 360's drive but I cannot look on that day no longer...it hurts too much...
So yeah, go buy an N64.