I can't just name one... it's impossible. Instead I'll list what games I can think of, in no particular order -
Champions of Krynn
Ah, the good old SSI AD&D games - a golden age in western RPG's. I spent six months on this game, mostly because of the cities and dungeons I traipsed through had identical walls and what-not. I still remember when my Knight of the Crown became a Knight of the Rose through a series of challenges that proved incredibly tough - only one member of the party could choose to complete a trial, and if it was anyone but the knight, they would die... until the end, where they would all magically come back to life.
Years later, when people were raving about this game on the PlayStation called Final Fantasy VII, I managed to rent both the machine and the game out and I was not, to say the least, impressed. It had exactly the same random enemy encounter gameplay I'd seen in Champions of Krynn almost a decade earlier. Talk about your next generation...
Flimbo's Quest
This was one of four games (the others being Fiendish Freddy's Big Top O' Fun, Commodore International Soccer and Klax) that came on the C64 GS cartridge. When the GS failed, Commodore got rid of their surplus by releasing the GS cartridge with regular C64's, and I managed to get one from a friend. My sisters
adored this game, and played it as often as they could - in fact, I still have a C64 today (with a 1541 Ultimate II, naturally) and at a recent family gathering I brought out my C64 and they were delighted, playing Flimbo's, Fiendish Freddy, Mayhem...
A fantastic little game with some of the loveliest tunes the SID chip ever produced, it was a platforming game whereby you had to kill certain monsters that carried scrolls - each scroll carried a letter which you brought back to the shop... once you had enough letters, you progressed to the next level. Inside the shop you could also buy upgrades to your pea-shooter alike weapon, such as a faster rate of fire, a longer range before it dissipates, extra time, invulnerability, even buy the next letter. Great little game.
Bubble Bobble
God, who didn't love this game? Bub and Bob, the boys turned into adorable little dinosaurs, would go on to star in two sequels (Rainbow Islands and Parasol Stars, the latter of which would sadly never come to the C64 due to, of all things, a spousal disagreement), as well as be used in the Puzzle Bobble aka Bust-A-Move games in the last decade. A simple concept, it was very fun to play and could become infuriatingly difficult in the later stages. One of the best multiplayer games on the system.
Guild of Thieves
Ah, text adventure games. I didn't like most of them, as they usually had dim or non-obvious parsers, and many of them didn't have very good stories to tell. Along comes Rainbird, a subsidiary of the once-famed game company Firebird, with the highest quality text adventures I've ever seen. They did have a lot of disk access time, but this was due to one of the most intelligent parsers I'd ever seen in such a game.
There were others that came before
Guild, such as
The Pawn (which I didn't own) and
Jinxter (which I did), but this was the first of the series I'd played and it left a definite mark on me. You should've seen the extras that came with these games, too - full size newspapers with hints for the game, nonsensical stories, images and the like... I used to show them to my parents once every few years, tell them I'd found these papers in their room, and what the hell were they? Just to confuse them. The looks on their faces as they read through them... Even with today's special editions, you don't get this sorta stuff anymore.
Rodland
Like Bubble Bobble, another platform arcade game, Rodland was probably my first encounter with anime/manga style character design long before I realised it. You played as Rit (and a friend played as Tam, her sister, if you played multiplayer) who was out to rescue her mother, and she did so by bashing enemies heads in using a magical rod, which also allowed you to create ladders you could use to reach platforms. Levels would end either when all enemies were dead or you collected all the flowers. Again, simple in concept, fun to play, bloody difficult in the later stages.
Ghostbusters
I can't do a favourite C64 games list without mentioning this, the game that got me to want a C64 in the first place. I didn't have much exposure to computers and consoles as a child - the recession in 80's Ireland had hit us hard and very few people had money. The only computers I experienced were the Apple IIe at school and the Atari 2600 people were still using and buying in the late 80's and early 90's. I wanted an Atari 2600 for Christmas, I remember, but one day our parents took us up near the city to visit some friends of theirs, that we as kids had never met before. As the adults wanted to talk, we were directed to their son's bedroom, where he and his brother were playing a boring looking shooter on a computer.
After a while he let us play, and he loaded up several games, though I can only remember two - this and Yie Ar Kung Fu. Both games wowed me - but it was Ghostbusters that made me wanted to get a C64. Ray Parker Jr.'s excellent tune instantly recognisable coming out of the SID, buying additions to my arsenal, driving through the city in ECTO-1 and capturing ghosts (and not crossing the streams!). I never did beat it, for some reason, but my memory of that day is very strong, thanks to this and Yie Ar Kung Fu. That year I did get a C64 for Christmas, along with a 17" black and white television all to myself. I was in heaven.
Mayhem in Monsterland
Oh, this game. The Rowland brothers had previously wowed C64 users with Retrograde and their famous Creatures and Creatures 2 - Torture Trouble, and with this they really brought their A-game. Everyone loved Creatures, and I was no different, but the little guy you played as, Clyde Radcliffe, moved in a somewhat stiff way - he wouldn't jump and run, he would jump or run, so there was a lot of stopping and starting. Compared to Mario and Sonic, he seemed somewhat pedestrian. And then along came Mayhem.
Mayhem was designed to be, as C64 magazines called it back then, more "console-esque". This was in the early 90's when 16-bit platformers were all the rage, and they were being made by seemingly every developer under the sun - the market was flooded by pale Mario and Sonic imitations. The Rowland brothers, John and Steve, decided to create their own game that would match the 16-bit console games' speed and fluidity - Mayhem would be as fast as Sonic, they said. And not only that, but it would look like no C64 game - it would look just as good as those 16-bit platformers on the SNES and Mega Drive. How?
There was something on the home computers back then (and still today) called the demo scene. Demos were a group of collated graphics and music and effects, which were designed to show off a programmer, graphician or musician's skills. Groups would challenge each other by doing things that hadn't been done before, like taking advantage of bugs in the VIC-II graphics chip to remove the borders, or mix colours to get more than the 16 the C64 could output. These techniques had been done in demos for years, but hadn't really shown up in games yet. Thus the Rowland brothers took advantage of many of these tricks, such as the ones I mentioned, to create a game that would at least match the 16-bit platform games.
The result was magic. Magazines gave it extremely high scores - 97% from Commodore Force, and even a very foolish 100% from Commodore Format. It deserved the former, at least - Mayhem is a very, very good game. It does indeed look like a game you'd expect from that era on the Mega Drive, at least. And with the lightning bolt power-up, Mayhem sped up to run about as fast as Sonic did, at least in the original game (and Sonic scrolled in eight directions, Mayhem only in two - hey, there's only so much an 8-bit machine running under 1MHz with only 64KB of ram can do!). A classic, it was released on the European Virtual Console store on the Wii, and I believe a mobile version was also produced a few years ago.
God, so many more I could list... maybe I will, later.