This list will get long, most likely. This is a comprehensive list of the greatest games of all time. Period. If it isn't on this list, it sucks and isn't worth playing anymore. All of these games are still fun to play at the moment and will continue being fun to play for eternity.
PC:
Fallout 1 and 2 (2 of the greatest games ever made)
Duke Nukem 3d
Command and Conquer Red Alert (2 was pretty good as well, but fuck 3)
Sins of a Solar Empire
Galactic Empires 2
TES: Daggerfall
Half-Life
Counter-Strike
Guild Wars (though, I don't play much anymore, I still pull in a few hours a month)
Diablo 1 and 2
Starcraft
Final Doom
Homeworld
Syndicate
Icewind Dale
Tribes
Freespace 2
Max Payne 1 and 2 (best 3rd person shooters ever made)
And now to move on to the less superior systems:
NES:
Final Fantasy 3
Punch Out
Dragon Warrior 4
Prince of Persia
Ninja Gaiden
SNES:
Final Fantasy 6
Gradius 3
UN Squadron
Earthbound (Mother... whatever the fuck you people call it these days)
Chrono Trigger
Genesis:
Phantasy Star VI
Mutant League Football and Hockey (still the most fuck awesome sports games ever released)
Shadow Run
Shining Force
Sega CD:
Lunar: Eternal Blue
Sega Saturn:
Dragon Force
Panzer Dragoon Saga
Playstation:
Metal Gear Solid
Final Fantasy VIII (Fuck your seven, bitches. 8 has 2 things 7 was missing that made it not so good: Engaging stat mechanics and A DECENT FUCKING PLOT)
Ehrgiez (not the fighting mode, just the super awesome dungeon crawl bonus RPG)
Dead or Alive (still play it actively today)
Soul Blade (the only good one in the series)
Silent Hill
Resident Evil 2
Persona 2 (either version, granted, I didn't play the non-localized half till last year)
Raystorm
The PSX rocked.
N64:
Legend of Zelda: Ocarnia of Time
Pokemon Snap (FUCK YOU)
Dreamcast:
Phantasy Star Online
Jet Set Radio
Crazy Taxi
Shenmue
Skies of Arcadia
Grandia 2
Dead or Alive 2
Bangai-0
Rez
Dreamcast was the most kickass console system ever. Period.
PS2:
Persona 3
Persona 4 (yeah, kinda newish to include on this list, but fuck you... Social links)
Shin Megami Tensei: Nocturne (you can fucking KILL GOD. Enough said)
Disgaea 1 and 2
Shin Megai Tensei: Digital Devil Summoner 1 and 2
Yakuza 1 and 2
Valkryie Profile 2 (seriously underrated by the fags)
Star Ocean 3 (Just after ripping on FF7 up there I include this?! Well, it's a solid game gameplay wise. Sure, the ending was completely fucked, but it had nearly a hundred hours fun GRIND)
Silent Hill 2 (Saved this for last... the greatest Survival Horror game ever made. I play it once a year on release date. It's an odd ritual)
Gamecube:
Resident Evil 4
XBAWKS:
LOL (Honestly, there is not one single game on this system worth HALF A SHIT that wasn't ported)
PS3:
Valkyria Chronicles (The only game on the PS3 worth playing. Even Disgaea 3 wasn't that good.)
Wii:
No More Heroes (FUCKAWESOME. Pure FUCKAWESOME.)
Madworld (Little early, yeah, but... PURE FUCKAWESOME ALSO)
Xbox 360:
Lost Oddessy (This game was down rated for NO FUCKING REASON other than square and PS3 fanboys pissed off that all the good portions of the early FF teams made this game. After their successors made the steaming pile of shit that was FF12, it was nice to know that these guys are still competent as ever releasing a great RPG with a very great story)
And there you go. Handhelds are gay.