Sonic 1 on the Megadrive.
Cannon Fodder on the Megadrive
Lotus Speed Challenge Racing on the Megadrive (I think that was the name I remember it was a Racing game with Lotus)
Streets of Rage on the Megadrive
Tetris on the Gameboy.
Mario on the Gameboy.
Afterburner on the Master System.
Legend of Zelda on Gameboy.
Final Fantasy Legend 3 (actually the very first FF game I ever played and not one of the main series)

Each of the above games could claim to be some of the first games I ever remember playing and thinking trout I needs me some of this!