Most of the good games are STILL good games today, and not because of the nostalgia factor. Simply good gameplay and design.
Squish 'em - Possibly my favorite game and the one I was ACE at. Far subtler gameplay than what it seems.
https://www.youtube.com/watch?v=GaN0vyguor8
Bruce Lee - One of the very best. Immensely fun just to mess around with two players in the first two screens. Me and my cousin playing just THAT for hours. It took us a while even to figure out that a secret passage would open. The rest of the (rather big) game was entirely optional.
Who Dares Wins - A Commando clone, but still rather good. My shooting game of choice.
Ghost'n Goblins - For obvious reasons, though I was a kid and rarely even made up to the second map.
Zaxxon - Another true classic, my first shooter. Incredibly hard because you had to figure out isometric and controls and the subtle height guesswork.
Boulder Dash - Another super classic. One of my friend would ONLY play this game. Just this one, forever.
Shamus Case II - One of my most played game. Again I didn't go very far, but so immensely playable and so fast.
Raid on Bungeling Bay - Super classic. Awesome gameplay. I'd play for hours with friends or not, without again any clue about the actual game's goal.
Falcon Patrol - Arcade airplane, very good and challenging game, the most dangerous thing was refueling.
Suicide Strike - One of the very best shooters along with the others I listed. Very good gameplay and simple.
Forbidden Forest - Super classic. Try to play this as a kid, it was super-frightening. Awesome sound.
Dig Dug - Do I need to explain?
ChipWits - My first "programming" game. Insanely complex for a kid, in fact I never really manage to achieve much, but it conditioned me deeply and still today I'm fascinated by that kind of complexity.
Omega - another programming game where you'd code a tank AI. Lots of disk swap and way too complex for me. The manual was HUGE. Actually more than one. There was a whole programming language created for this, and you'd have to build the tank, buy components and challenge other AIs. Even making past the welcome screen, formatting the "save" disk and everything took me a day. Just absurdly complex. I think even Garriott had his hands in this.
Gauntlet - A classic. Playing with 2 players it was basically god mode since you could resurrect as long one player was alive. Though I think I got only close to level 100. Without being able to save getting far would take forever.
Gumshoe - Lesser know title that was AWESOME. You had this big level with elevators and doors and you'd go around in non-linear ways, with always a great tension. Very sleek design.
Cæsar the Cat - Simple game, endlessly playable. Way too charming.
Orc Attack - Another super favorite of mine. Lesser known and simple, but exhilarating gameplay (especially the bodycount at the end).
Sword of Fargoal -
https://www.youtube.com/watch?v=nIuMUIzxrLs My first roguelike. I played this for so many hours, but without really going far into it.
Mancopter - FLAPPY BIRD precursor. But actually great game, really.
https://www.youtube.com/watch?v=YhaARqv1Ol0
Star League Baseball - Simple and very fun. Way too many hours spent on this, even if I barely grasped the game. I'd just lose horribly.
Pitstop I & II - The driving games. Though my favorite was another I can't find now.
Super Cycle - Like Pitstop, but with motorcycles.
Quake Minus One - The game I'd play without ANY CLUE about what was happening or what to do. Absolutely nothing.
Terror of the Deep - As above, just WTF?!
Sky Travel - A planetarium. Absurdly rich.
The Duel -
http://www.lemon64.com/?mainurl=http://www.lemon64.com/games/details.php?ID=3926 I don't even remember if it had single player, but I absolutely loved to play this with a friend. Though I was too good and only one of my friend could actually challenge me.
ACE: Air Combat Emulator - My first flight sim! It was kind of crappy and you had to play with someone else controlling the cursor if you were hoping hitting something.
Ghostbusters - But I never even manage to capture one ghost or even figure out the game structure. I'd just use a cheat to have some money and build a good car, and the play the car section.
Impossible Mission - Another game you could play for hours without a clue about what you are supposed to do. Levels were randomized too so I'd play with a friend and just take turns at solving a room.
Alien Syndrome - A precursor to Amiga's Alien Breed.
Activision's Decathlon - Destroyed many joysticks.
Microprose Soccer - Because way too many hours playing the World Cup.
Bop'n Rumble - I didn't have Golden Axe or Double Dragon, so this was my brawler. Nice having every level change the moveset.
Gyruss - Classic great shooter. Though it can get monotonous.
Legend of Kage - another less known game with fun gameplay that I'd sink hours just sitting in the first screen and survive as long as possible instead of actually progressing. Really fun ninja game with crazy jumps that were more like flying between super huge trees.
Frogger II: Best Frogger? You could reach the sky, and there were dragons.
Silicon Warrior - Simple and addicting.
Silk Worm - Classic, very hard.
Little Computer People - Took forever to load. The Sims precursor and so charming and addicting despite being so boring. You always felt like it had so much hidden, but at the end interaction was fairly limited.
But I actually had the C64 long before the good game came out, so a lot of games are obscure and you can't find them even on the lists on the internet. I played obscure text adventures, or the likes of Aztec Tomb Adventure
http://www.gamebase64.com/game.php?id=519 There was at some point a complete playthrough on Youtube, but it's sadly gone.
A few of games that I always wanted but I wasn't able to buy: Wasteland, Deathlord, Bard's Tale, Neuromancer, Ultima, Halls of Montezuma, Elvira, Times of Lore.
