Project: Firestart
An adventure game that sets you alone on a space station where a biological experiment has gone wrong. There are a few endings depending on what you do before you set the self-destruct and leave the ship. Don't try and kill all the dudes, they'll keep coming. Shoot a path and make a run for it. With its atmosphere and style, this is easily what one might be tempted to call a survival-horror game. Go get the map from gamefaqs, it's not cheating, it was included in the manual and is essential to enjoying the game.

Enforcer: Fullmetal Megablaster
Despite some sprites ripped from a previous port of R-Type, this is one of the best looking shooters on the 64. It has very fast action, with hoards of enemies, some very large. Luckily one hit does not kill you, and there's a shield power up. The power up system is sort of a weird Darius hybrid. There's also a charge shot like in R-Type. Technically it's pretty impressive for a 64 game, with dynamic backgrounds and a nice use of interrupts to play music and sound effects at the same time.

H.E.R.O.
HERO is a fun game, you play a guy with a helicopter backpack who must save people from within a cave. There are lots of traps, so be careful when entering that next screen. Intelligent use of dynamite is a must. Touching a red wall means death, so don't get to close.

Bruce Lee
In Bruce Lee you navigate a temple collecting lanterns while fending off baddies. There is a big map so there's plenty to explore. Excellent fun. The difficulty ramps up gradually, and it ends up being quite the challenge, but if you beat it you might think it was too short.

Into Oblivion
I am a glutton for punishment, so IO is my bread and butter. I've been playing this game for a while yet only in recent times have been able to beat the first level! This is a brutal shooter, an I have no right expecting any of you to like it, but I do. Some tips: The pick-ups you see kill everything on the screen unless you shoot them and turn them into power-ups. Collect power ups and you'll obtain little orbs that fly beside you, at this point getting hit takes away an orb instead of killing you. Also it's is advisable to simply fly up and avoid the first wave of enemies that fly at you, trying to shoot them down is a death wish.

Wizard's Crown
I was tempted to leave off RPGs since many 8-bit computer RPGs are too slow for many of today's gamers, but Wizard's Crown deserves attention for a combat system that rivals anything today in terms of complexity. A single fight can take you thirty minutes to play if they throw a lot of baddies at you. Not much in the way of story in this game but it's all about the combat. Downloading a manual is essential to understanding how it works. Knowing things like spears go over allies, axes break shields, flails ignore shields, and how facing affects what side you are protected on by your shield are important to victory.
Sentinel Worlds: Future Magic
An then I decided to include another RPG. This one has a space part where you move around communicating with other ships, disabling pirates and boarding them, and all sorts of cool space stuff. Nice story too. A manual is required for enjoying this game obviously, and along with that you get a paragraph booklet that you refer to when the game tells you.

Honourable Mention:
Shooter - Armalyte, Blue Max,
RPG - Alternate Reality, Telengard
Adventure - Below the Root, Sword of Kadash
Platformer - Turrican, Montazuma's Revenge, Hero of the Golden Talisman, Jumpman
Other - Hunter's Moon, Paradroid, Samurai Warrior
Ones I didn't mention cause they're the popular ones:
Last Ninja
Wizball
Great Giana Sisters
International Karate
Okay, I got that out of my system.