These may include my personal bias and reflect parts of my personal collection that I feel are important. Though, I don't own some of the game's I've mentioned here, the ones I am missing are sort of goals for me to work toward. I'm not mentioning the 360, PS3, Wii or 3DS in the list at all
NES - Legend of Zelda, Metroid, Batman, Mega Man 2, SMB3, Castlevania III, Dragon Warrior IV
SNES - Super Mario World, Yoshi's Island, Chrono Trigger, FFII & III, Secret of Mana & Super Mario RPG, Castlevania: Dracula X, LoZ: Link to the Past
N64 - LoZ: Ocarina of Time, Castlevania, Goldeneye, Conker's Bad Fur Day
GC - Animal Crossing, LOZ: Wind Waker, LoZ: Twilight Princess (The true version of the game), MGS: The Twin Snakes, Super Mario Sunshine
Game Boy - Tetris, Super Mario Land 2, LoZ: Link's Awakening, Final Fantasy Legend 1,2 & 3, Metroid II, Pokemon: Red/Blue/Yellow
GBC - LoZ: Oracle of Ages/Seasons, LoZ: Link's Awakening DX
GBA - Golden Sun, Golden Sun: The Lost Age, LoZ: Minish Cap, Metroid Fusion or Zero Mission, Mario & Luigi: Superstar Saga, Castlevania: Aria of Sorrow
DS - Animal Crossing: Wild World, Castlevania: Dawn of Sorrow & Order of Eccelsia, Radiant Historia, Dragon Quest V.
Genesis - Shining Force 1&2, Sonic 2-3 & Knuckles, Castlevania: Bloodlines
Saturn - Guardian Heroes, Panzer Dragoon, Zwei & Saga, Dragon Force, Albert Odyssey & NiGHTS into Dreams... (and Christmas NiGHTS into Dreams...) & Retranslated Shining Force III (and parts 2 and 3)
PS1 - Metal Gear Solid, Castlevania: Symphony of the Night, Final Fantasy VII & IX, Legend of Dragoon, Tony Hawk's Pro Skater 2.
PS2 - .hack//G.U. trilogy (The original .hacks are good too, but G.U. upped the quality), Metal Gear Solid 3: Subsistence, ICO, Shadow of the Colossus.(I don't own either of the last 2, but have played some of them. They are both works of art)
PSP - LocoRoco 2, Patapon, Daxter, Castlevania: Dracula X Chronicles, Metal Gear Solid: Peace Walker.
Xbox - Splinter Cell, Splinter Cell: Chaos Theroy, Halo 2