If we're goin back:
NES:
Super Mario Bros 1/2/3, The Legend of Zelda, Maniac Mansion, A Boy and his Blob, Duck Hunt, Tetris, World Cup, Turtles, Track & Field
Gameboy (+ Pocket / Color):
Super Mario Land, Super Wario Land, Tetris, Harvest Moon, Pokemon Red/Blue/Yellow, Legend of Zelda: Links Awakening DX,
SNES:
Super Mario World, Super Scope 6, Legend of Zelda: A Link to the Past, Super Metroid, Terranigma, Chrono Trigger, Mortal Kombat II, Flashback, Unirally/uniracers, Pilotwings, Starfox, Donkey Kong Country, Street Fighter II, Super Mario Kart, Yoshi's Island
Megadrive:
Sonic the Hedgehog 1/2/&Knuckles/3d etc, Streets of Rage, Golden Axe, Shinobi, Altered Beast, Splatterhouse 2/3, Columns, Micro Machines: Turbo Challenge,
PlayStation:
FIFA Soccer 96 (later realised it was awful, but at the time "wow!"), Intelligent Qube, Metal Gear Solid, Resident Evil, Final Fantasy VII, Porsche Challenge, Soul Edge/Blade, Tekken 2, Gran Turismo, Wipeout, Micro Machines, Tomb Raider 1/2
Nintendo 64:
Mario 64, Legend of Zelda: Ocarina of Time, Legend of Zelda: Majora's Mask, Blastcorps, Goldeneye 007, FIFA: Road to World Cup 98, ISS64, Extreme G, Diddy Kong Racing, Mario Kart 64, Forsaken, Pilotwings 64, Star Wars: Shadows of the Empire (another I find horrible now but loved at the time), and Star Wars: Rogue Squadron
from this gen:
GBA:
Tony Hawks isometric games, Mario Vs Donkey Kong, Golden Sun, Final Fantasy Tactics Advance, Advance Wars, Legend of Zelda: The Minish Cap, NES classics on the move
Gamecube
Star Wars: Rogue Squadron II / III (Rebel Strike), Eternal Darkness, Resident Evil 1/Ø and the promise of RE4, Metal Gear Solid: The Twin Snakes, Super Monkey Ball 1/2, Legend of Zelda Four Swords Adventures, Mario Kart Double Dash!!, Metroid Prime 1/2, Legend of Zelda The Wind Waker, F Zero GX, Donkey Konga (PAL/US), Tales of Symphonia, Viewitful Joe, Phantasy Star Online
Dreamcast
Powerstone, Soul Calibur, Grandia, Quake III arena, Unreal Tournement, Ready 2 Rumble, Sonic Adventure, Jet Grind Radio, Samba De Amigo, Shenmue, Space Channel 5, Skies of Arcadia, Bomberman, Phantasy Star Online
Xbox
Jet Set Radio Future, Panzer Dragoon Orta, The Chronicles of Riddick: Escape from Butcher Bay, Splinter Cell, Ninja Gaiden
PS2
Metal Gear Solid 2, Grand Theft Auto III / Vice City / San Andreas, Final Fantasy X, Kingdom Hearts, Eyetoy Play / SEGA Superstars
Dreamcast & Gamecube have been most fun for me personally this gen.