Halo 2! it perfected the FPS on consoles and incorporated by FAR the BEST online multiplayer for a game on consoles. Infact games havnt evolved very much since and it still holds up extremely well.

Super Mario RPG. It was fun. It was funny, the graphics were amazing, its spawned two RPG series (Paper Mario + Mario & Luigi) totalling 6 games. There's really nothing else to say about it other than it was a blast to play, and loved every moment of it.

Doom. As if it needs an explanation, this is one of the most absolutely influential games ever, having better puzzles then most modern day games (and pretty much ALL modern day shooters) tight action, fantastic online(it also started "fragging", and the FPS genre having online)

Doom is, has been, and always will be one of the most insanely influential games of all time.  And one of the best.

Hmm thats a tough one.It would be between gunvalkyrie ,dead or alive 2,jet set radio or tales of vesperia. Gunvalkyrie extremely fun while being challenging,Dead or Alive 2 is a complete blast alone or with friends with its high speed gameplay,Jet Set Radio cuz it oozes style and it has fun tagging/races, and Tales of Vesperia...well i just liked every aspect of it.

Metal Gear Solid 4: Amazing visuals, perfect gameplay that can be played in multiple ways, Hollywood-like production values and the end to the most amazing saga ever. Plus, this game made Snake truly legendary! The game also has some amazing moments, like the microwave scene, the slow motion sequences during the act 3 chase, all the boss fights, the battles in act 1 and 2, playing as REX, the graveyard scene, Otacon's explanation to Sunny about what happened to Snake, and there are so many more, I just can't remember them off the top of my head, it's 3am here :P. Anyways, for me this game will truly be the greatest and no game in the future, not even another MGS game can be as good as MGS4 for me, mainly because Snake will be absent from them. I doubt anyone can create a game with a character as compelling as Snake.

Gonna have 2:

halo3 - multiplayer is beyond epic! I must have spent 1000s of hrs on this game! Nothing is more fun its so un scripted 2games are never the same!

And

street fighter - "spinning bird kick" been playing sf since day1 the art work story comics animated moves AND games massively influenced me into what i do for a living now! Plus the games have historic staus but can still progess into the 21st century

Lufia 2 is my all time favourite, with Terranigma and Parasite Eve a close second and third. These games are the epitome of RPG gaming to me, each one perfecting a different area of JRPG, be it Turn-Based with Lufia 2, full blown action RPG with Terranigma and Active Time Action RPG with Parasite Eve, and on top of that, each game had a story that would blow your mind with it's complexity and complete awesomeness ;):