The first computer I owned and loved was the C64 and I had it for much of my childhood, so many of my best game memories are related to it.
The Way of the Exploding Fist - Got a high score for this that appeared in the Aussie edition of PCG. Still remember all the different tunes as well as the way your man would scream when you did a flying kick or the way your opponent would groan when you low punched him in the guts.
Boulder Dash - First C64 game on tape I ever bought (well my Dad bought it actually, although I did have $20 in coins with me at the time!). Probably the first game I ever "clocked" too. Vividly remember all the different sound effects like the boulders falling, the amoeba growing, and the explosions that produced diamonds. Game was quite maddening on later levels as you really had to think quickly on your feet, otherwise you would die, run out of time, or become trapped. It was probably the intellectual challenge of this game that made it so memorable for me.
H.E.R.O. - Great little game. Involved manouevring your man with a jetpack around the place blowing up walls and creatures in caves with dynamite to save miners (?). If you didn't move far enough or quick enough away from the dynamite once you lit it then you'd blow yourself up and lose a man.
Pastfinder - Very underrated arcade-like game. It was the silky smooth speed of the gfx in this shoot-em up that sticks out in my memory.
Impossible Mission - The speech and the fluent animation of the main sprite were amazing and unforgettable. Also was a devilishly hard but addictive game at the time.
Rock 'n' Wrestle (aka Bop 'n' Wrestle) - Released in the days that WWF was really popular here in Australia. Played it many times, even after I'd beaten the game. Being able to perform the moves like the wrestlers on WWF made it such an awesome game back then.
IK+ - Released before Fist II and it really was the spiritual sequel of Exploding Fist for me. Sound effects were superb and the very act of fighting two opponents at once was sheer exhiliration (could often feel my heartbeat pulsating through my body), not to mention ground-breaking for its day.
The Last Ninja - Literally salivated over the screenshots in Zzap!64 for many months before it was finally released. Had the tape version on order for almost as long. Wasn't disappointed when I finally got my hands on it. The attention to details of the gfx was astounding for its day. I could sit there for minutes at a time looking at some of the screens in this game. Game also had about 12 tunes - one for each level and another that played whilst levels were loading. The tunes were pretty good, so much so that I hardly minded the tape multi-load.
Hypersports - Awesome sports compendium game. Felt like I was playing the arcade machine. So many cute touches in this game that was icing on the cake that was playability. Also unforgettable was the Chariots of Fire soundtrack on the tape loader of this game (Hyperload??).
These are my most memorable games for the C64 by virtue of the fact that I hardly paused to think while I typed this post.
I have some great memories of Amiga games too, but I think that I'll save them for another post.
Killer idea for a thread KG!