Looking back over the years I've noticed the first game you ever get whenever you get a new gaming system is usually unforgettable. For me it was a combination of excitement over a new system and the fact that I would be broke and only afford a game or two for awhile. List your systems and the very first game or games you got with it if you can recall.
NES - Super Mario Bros./ Duck Hunt
Gameboy - Tetris
SNES - Super Mario World
Genesis - Sonic the Hedgehog 2
Gameboy Advance - Bomberman Tournament
Nintendo 64 - Super Mario 64
Playstation - Final Fantasy 7
Dreamcast - Soul Calibur
Playstation 2 - Metal Gear Solid 2
Gamecube - Metroid Prime
Xbox - Halo
Nintendo DS - Mario Kart 7
PSP - Crisis Core: Final Fantasy 7
Xbox 360 - Elder Scrolls IV Oblivion
Wii - The Legend of Zelda Twilight Princess
PS3 - Metal Gear Solid 4
3DS - Fire Emblem Awakening
PS Vita - Ys Memories of Celceta
NES - Super Mario Bros./ Duck Hunt
Gameboy - Tetris
SNES - Super Mario World
Genesis - Sonic the Hedgehog 2
Gameboy Advance - Bomberman Tournament
Nintendo 64 - Super Mario 64
Playstation - Final Fantasy 7
Dreamcast - Soul Calibur
Playstation 2 - Metal Gear Solid 2
Gamecube - Metroid Prime
Xbox - Halo
Nintendo DS - Mario Kart 7
PSP - Crisis Core: Final Fantasy 7
Xbox 360 - Elder Scrolls IV Oblivion
Wii - The Legend of Zelda Twilight Princess
PS3 - Metal Gear Solid 4
3DS - Fire Emblem Awakening
PS Vita - Ys Memories of Celceta