Ahh, a good topic indeedy!
River Raid. First time I ever saw a videogame at home. That bitch hit me HARD.
Commando, Monty on the run, Giana Sisters. To name but three C64 influences. I know all the bloody songs off the top of my head. I presume all these blippybloppy sounds are the creators of my musical tastes of today.
Lemmings 2, wing Commander, Turrican 2. First games I ever saw running in MY Amiga. Turrican 2 was a fucking gobsmack. Oh, and so was Lotus Turbo Challenge.
There are lots of others, I think most games I have played have influenced me life a lot. I cannot go away without mentioning Sonic 2. Played that nbastard religiously everyday for at least 6 hours straight., I know all the levels, musics and tricks like myself.