Bubble Bobble was a huge one for me. Me and my sister used to play it for hours on end.
Another one would be Red Alert. I came accross that game when I was in the 4th grade and me and my friend played it every day after school over our l33t 28.8k modems.
Another great game I spent years playing is Dark Forces II: Jedi Knight. The game was so open, so easily hackable. Not hackable in a bad sense, but in a fun one, like being able to build things. Spawn tables and environments, make your own house, in essence just like Garry's Mod. I also played countless hours of SaberBattleX, a mod for the game, that added sweet models, fun jedi moves and better lightsaber graphics. I played that game until the Multiplayer service that carried it, MSN Gaming Zone, dropped it like the fascist bastards they are. Much like how Gamespy stole my beloved MPlayer... RAWR NOW I R ANGRY! TASSADAR SMASH! TASSADAR SMASH! TASSA..derr... *falls asleep*.