Well, seems like every time one of these threads comes around, I post the same links. Get ready, because this time is not exception.
http://c64.emucamp.com/ is a link to Lemon’s C=64 site. Actually, no it’s not. It’s a link to a site saying “this site has moved!” and linking to Lemon’s site. But I’m too lazy to fix it right now. Cope.
http://arnold.c64.org/ is the Arnold database of Commodore programs.
http://ltd.simplenet.com/c64/games/a/ is even more fun stuff.
Anyway, get yourself a Commodore emulator. CCS64 beta is probably the best one out there. Once you’re fired up, get ready to play some Paradroid, Bubble Bobble, or whatever else once again! Actually, I’ve downloaded several hundred games since getting the emulator and most start to get old fairly soon, but Paradroid remains a classic in my book.
Other classics:
Mail Order Monsters: Order yourself a beastie from the catalog and equip it with various weapons, supplies and genetic traits. Then send it out to kick some butt for cash so you can buy more of the above.
Archon: Sort of a fantasy chess game where good battles evil. Played on a chess board, the pieces actually fight when they go onto the same square. Not staged fighting like Battle Chess, but actual joystick controlled combat. I used to be able to beat this game with White in about 5-7 moves when I wanted to. I believe it was Elemental on Shape Shifter, Teleport Unicorn onto Dragon (or shifter if Sorceress raised it from the dead), Unicorn onto Sorceress, grab the other “spot” squares while Black feebly sent goblins and stuff against your unicorn. The unicorn was fast and strong enough that with a little practice at sniping from behind the “trees”, it was easy going. By the way, the IBM version of this game sucked. I think the phoenix was still able to be hit while flaming, so it was less useful than the banshee (which black got two of). Ok, I’m getting off topic here…
Adventure Construction Set: What a good time. Build an entire world to adventure through and set it up in any period or genre that you wanted. I made an adventure based off of a fantasy series that was amazingly true to the books that I’m still proud of. The ony thing keeping me from downloading it onto the emulator is that I don’t think I could find anyone who’d actually want to play an ACS adventure today 
Racing Destruction Set: Create a track using various heights and jumps, curves, etc. Make it dirt, asphalt, ice or any combonation of the three. Customize cars to drive upon it and give them armor, crushers, oil to spill or leave them without any of that if you wanted speed. Set the gravity to anywhere from Jupiter’s to Io’s. Then let 'em rip!
I could go on and on, but I’ll let others have a say.