I'll bump it, and post later. Nice thread Kyliedog.
NES: SMB2
SNES: Mario World
N64: Mario 64
GC: MM (on the colector's edition)
First gen: ...Pong?
Second gen: Adventure
Third gen: Super Mario Bros. 3
Fourth gen: No....don't make me choose. Super Mario RPG I suppose.
Fifth gen: Picking favorites get progressively harder with each generation. Final Fantasy 9.
Sixth gen: Okami
First Gen: Pong
2nd Gen: Space Invaders
3rd Gen: Super Mario Bros. 3
4th Gen: Super Mario World 2: Yoshi's Island
5th Gen: The Legend Of Zelda: Majora's Mask
6th Gen: Resident Evil 4
7th Gen: Metroid Prime 3: Corruption
well, it would take too long to list games from all the systems I have owned or still own, so I'll just go by generations.
Genesis/32x/cd/NES= Shining Force
Shining Force is one of the greatest Strategy RPG's ever made. I still pull out it out to play. Had fun gameplay, epic story, and Jogurt :)
Sega saturn/psone/N64 = Suikoden II
This may be the greatest RPG of all time. Tons of characters to find and all have a unique story. The story is beyond epic and I love how they developed the relationship between the hero and his pal/enemie. Moon Bird Recipe FTW!
Gamecube/Ps2/Xbox = Star Wars: Knights of the old Republic
This was a hard one for me. There wasn't one game in this generation that just screamed at me as the best. However, seeing as I have replayed this game like 15 times I figure it has earned it's place as best of the generation more than any other game.
wii/Ps3/Xbox 360 = Valkyria Chronicles
What can I say, I love Strategy RPG's and this one delivers. This was a tough one because there are a lot of games I love this generation, but Valkyria is just that good.
GBA/DS/PSP = Shining Force: Return of the dark dragon
I just lumped the handhelds into one category. I know this is just a remake of the original game on the genesis, but with updated graphics, new characters and maps, this remake brought new life and joy back to my life.
I wish Sega hadn't destroyed the shining force franchise by taking it away from it's SRPG roots, but oh well. This is my list of favorite games for each generation. If you want to look at what other games I have, I have them all uploaded to my profile 
Pre-NES/NES
Amstrad CPC464: Bomb Jack- I used to go home from school and play this game all day, I even got my mum playing this game!
SNES/Mega Drive
SNES: Super Mario World- Yoshi was kinda cute and a cool addition to Mario
PC: Duke Nukem 3D- Hail to the King baby! :P
PS/N64/Saturn
PS1: Tomb Raider (Intelligent 3D platforming), MGS1 (Amazing story), Tekken 3 (Dunno why but Tekken games have always struck a cord with me) and Final Fantasy VII (first JRPG)
N64: Goldeneye, Lylat Wars, F-ZeroX- These 3 because of great 4-player split screen parties.
PC: Half-Life (story and nothing quite like it before), Age of Empires (Really well-balanced RTS, the whole time period also appealed to me)
PS2/X-box/Gamecube
PS2: MGS3 (story), GTA: San Andreas (The sheer scale and the variety of vehicles)
PC: Deus Ex (best game ever, amazing story, lots of player choices... a genre melding game of brilliance), Age of Empires 2 (amazing online battles), Morrowind (Great open-world RPG, the art styles were quite unique), Neverwinter Nights (Good-solid RPG, played the expansion packs over LAN with my partner), Call of Duty (loadsa LAN battles in my halls at Uni!)
Wow, thats more then I expected, lol.