I hope I remember all the great games I've played way back since the SNES days...
Super Mario Bros 3 (Super Mario All Stars) SNES
Super Mario World
Donkey Kong Country 2 (Best platformer ever created)
Mortal Kombat (old and 2011)
Mortal Kombat 2
Mortal Kombat 3 and Ultimate Mortal Kombat 3
Mortal Kombat Trilogy (loading times on PS1 sucked hard though. Also, the gore effects were loltastic)
Tetris (fuck yeah)
The Legend of Zelda A Link to the Past (best one, fuck the others)
Super Bomberman
Super Bomberman 2
Twisted Metal 2
Twisted Metal 4 (played this quite a lot even though nowhere near as good as TM2)
Twisted Metal Black (First PS2 game - holy shit, an M rated Twisted Metal game!)
Twisted Metal Head On
Twisted Metal PS3
Gran Turismo series (3 and 5 the top ones)
Crash Bandicoot 3
Vigilante 8
Sypro Year of The Dragon
Jak and Daxter
Daxter
God of War franchise
Kingdom Hearts I and II
Grand Theft Auto San Andreas
Grand Theft Auto Liberty City Stories
Grand Theft Auto 4 + Ballad of Gay Tony
Silent Hill Origins
Silent Hill
Silent Hill 2
Silent Hill 3
Parappa the Rapper
Need for Speed Underground
Medal of Honor Frontlines
Dance Dance Revolution 1st mix to Extreme (Japanese versions. All US versions sucked donkey dick and the newer ones were hit or miss)
In The Groove arcade
Pump it Up arcade
DJMAX Portable Black Square
DJMAX Technika arcade
Beatmania IIDX arcade
DJ Hero
Rock Band
Uncharted series
Infamous series
Batman Arkham Asylum and Arkham City
Need for Speed Hot Pursuit - a Criterion game
Killzone 2
Metal Gear Solid 4
Bad Company 2
CoD 4 campaign
CoD World at War online
Resistance 3 campaign
Assassin's Creed 3
Blur
Dead Space games
Far Cry 3
Portal 1 and 2
All of these I enjoyed very very much. Probably missing a bunch of stuff htough.