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Snowboard Kids- Really fun unrealistic game from Atlus. Controls are great and the multiplayer is very fun. The sequel is also good, but I prefer 1.
Ogre Battle 64- One of the N64's 2 good RPGs, and a damn good one. A mix of real time strategy and tactical RPGs, it's a very deep and long game that can easily stand up to the best PS1 RPGs. Steer clear if you're not a big fan of strategy RPGs, but a real treat if you are.
Paper Mario- The N64's other good RPG. Not the hardest game around, but the battle mechanics are deep and fun, the dialog is funny, and the Mario universe perfectly suits the game rather than feeling like an afterthought.
Space Station Silicon Valley- Made by the people who would later make Grand Theft Auto, this is a bizarre and twisted platformer about killing animals and taking control of their bodies. Flawed, but memorable and ambitious.
Mischief Makers- An awesome 2D action game by legendary developer Treasure, there's nothing else quite like it. Received mediocre reviews at the time but retrospective reviews have been very positive.
Wave Race 64- Perfect game to turn on for a few minutes whenever you're looking for a quick dose of fun. Controls extremely well and the summer setting is nice.
Pilotwings 64- A "flight sim" where you fly around in different vehicles. There are various objectives to complete with each, but the controls are good enough that it's even fun just messing around aimlessly.
Micro Machines 64 Turbo- A completely wild top down racer. A great 4 player game, and it even lets you play 8 player by sharing controllers.
Blast Corps- Drive around in various demolition vehicles/robots with the goal being to destroy everything in the path of a rogue bomb carrier. You'll need to quickly master the controls to succeed but the game is fun and very fair, and you feel so good every time you beat a level.
Ridge Racer 64- I'm surprised no one ever talks about this game, it's a lot of fun. Fast, smooth, arcade style racing.
Bomberman 64- Somewhat different from traditional Bomberman games, plays like an adventure puzzler rather than the standard arcade action. Still a great game, with an awesome battle mode too.
Diddy Kong Racing- Mario Kart 64 is probably the best 4 player racer on the system, but for single player this game is way better thanks to an actual story mode and very good controls and tracks.
Dr Mario 64- An almost completely forgotten game, it's a fully featured and well polished game that's definitely worth checking out if you're a fan of Dr Mario or other falling block puzzle games.
F Zero X- I used to be obsessed with this game. Calling it smooth and fast would be an understatement, and the tracks are crazy like roller coasters. One of the best uses of the rumble pak too.
NFL Blitz 2000- The complete opposite of games like Madden, it's fast paced arcade style football with simple controls and a focus on fun. Another one of the N64's many great 4 player games.