Ok, where to start. There's many good C64 games, so do you have a genre preference?
There are the obvious ones like Impossible Mission, Summer/Winter Games, Turrican, Last Ninja, Giana Sisters, Uridium, Bard's Tale, Test Drive, Ultima, Speedball, IK+ and all of those.
I was always a huge fan of
Enigma Force, played it through at least once a week, once you get the hang of it, it's easy. Fantastic soundtrack too:
https://www.youtube.com/watch?v=wVnUphAGx0ENice Cyberpunk Adventure/RPG is
Neuromancer, which contains elements of several game genres. Complex game with some of the tougher puzzles.
Great shmups with great music are
Armalyte:
https://www.youtube.com/watch?v=lT3kmm8B_FE and
Katakis:
https://www.youtube.com/watch?v=_5GfqzS9Bog or
X-Out:
https://www.youtube.com/watch?v=Ahy_ADlFwlsSeven Cities of Gold takes you on an expedition in an adventure like game, always liked to play that one. And another game from the same guys is
Heart of Africa, worth checking out. Btw, they also made
M.U.L.E.Older multi scroller shmups is
Fort Apocalypse, just try to finish this one without using pokes, without throwing and breaking your joystick, aaaargh...
If you're looking for a good platformer, then I would recommend
Hawkeye, has also music by Jeroen Tel.
Knight 'n' Grail is also nice, released only in 2009.
Spherical is also nice, although a single screen platformer, plus you might favor the Amiga version.
Alter Ego isn't really a game, but a multiple choice simulator where you get born and start your adventure as a baby until your old and die. I played this quite often, as the out-comings are always different and it's really nice to continue and chose your own journey. There's a male and female version. In my opinion, an absolute must play game as it's very different, calming, and of course the girlfriend/wife will mostly enjoy it too.
If you wanna play a nice RPG, you can take any of the SSI games, like
Pool of Radiance, which are all based on the official Dungeons & Dragons rules. Favorites of mine in this category are
Champions of Krynn and the sci-fi
Buck Rogers - Countdown to Doomsday, all available on PC too.
Caren and the Tangled Tentacles is a Maniac Mansion type of adventure and came out in 2015.
Project Firestart is a nice adventure/action/shooter with a sci-fi setting and has kind of an Alien vibe, your research ship is called Prometheus!
If you like Karate games, there's
Way of the Exploding Fist, which in my opinion is the better International Karate,
Karateka by Jordan Mechner which has some really nice animations, and of course
Bruce Lee, which I wrote a review of.
If you like an experience like Elite, then
Tau Ceti is a must play. It's nicely done graphically in 3D.
Scarabaeus is a very nice 3D adventure game with some mysterious plot and setting, kind of like Maze Runner as a game. Very unique.
Another interesting game is
Infiltrator, an action/flying simulation with stealth when you enter bases. Graphics here are also very good. Which brings me to another interesting title,
The Train – Escape to Normandy. Let's put
R.M.S. Titanic also here.
Of course you will need to play
Law of the West, western themed game, where you play as the sheriff, go down the road of town and have to take some key decisions. Also very unique gameplay, if you can call it gameplay, as your main objective is to talk to people and make you decisions. Very creative, 3D ego shooter from 1985.
For me the best to date breakout style game is
Krakout, which has many enemies and bonuses and also has a little twist, it's played vertically.
Times of Lore is another nice action RPG with loads of content, and a fantastic long title music by Martin Galway, epic.
One of my favorite platformer, more puzzle oriented games is
The Castles of Doctor Creep, and it can get rather tricky, but a must have C64 game, in my opinion.
I guess Sid Meier's
Pirates! don't need to be mentioned?
Raid over Moscow was one quite politically incorrect game indexed in Germany, where you have to fly a fighter plane to the Kreml and destroy a reactor. The game is quite difficult, and straight in the beginning, when you have to fly your plane out of the hangar you know what I mean. Although once you manage, it will be easy afterwards. Same company, Access Software, also released the 2
Beach Head games, part of their war themed games, which are also worth a look.
Another one comes to mind immediately when mentioning the word "raid", and that is the great
Raid on Bungeling Bay, a multi scrolling shmups.
The Sir Arthur Pendragon series are also really good games, like
Staff Of Karnath,
Blackwyche or
Entombed, a mix of action, platform and puzzle.
A huge RPG is
Newcomer, which, when it came out was the largest game so far, taking the space of 7 disks. Very long animated cut scenes, which look awesome, and show what the C64 was capable of. Scary music will accompany the whole trip. The game itself is also VERY long.
My favorite game is probably
Racing Destruction Set, where you can build your own tracks, which leaves you with a cool construction kit and endless tracks. Best part was that you could build nice ramps, and depending on which planet or moon your track was set, low gravity made you jump like crazy, just mentioning Io and Callisto here. Me and my cousin spent months of building tracks and trying them out. Great game.
Fast Tracks might go in that direction, which the track building ability, but the driving itself is quite in-existing, as the car moves down the lane by itself, kind of.
Skate or Die! is a multi event sports game, consisting of several different disciplines. Great title music as usual from Robb Hubbard:
https://www.youtube.com/watch?v=XetgpWY7WOgDruid and
Druid II are some nice Gauntlet like "shooters" with focus a bit more on the role playing part.
I always liked
Waterpolo, a little sports game about... well water polo. That's my guilty pleasure, don't tell anyone though

I might come across more, as there are so many great games.