The N64 was the last cartridge based console I have bought way back in 1996. I initially purchased the Nintendo 64 console with two controllers and three games: Super Mario 64, Pilot Wings and Wave Race. These are still excellent games more than 15 years later and they all possess something many of today's modern games lack - fun and playability. Who cares about accurately rendered 3D environments and textures or 15 minute cut scenes - though some N64 games had these - but give me responsive gameplay any day!
1 Super Mario 64
Super Mario 64 contains 15 massive 3D worlds that are cleverly laid-out so that there's never a dull moment. Each world requires Mario to find seven stars, and also find a hidden secret star, in order to move onto the next area. This game recaptures the classic gameplay style of the original 2D series that was on previous Nintendo consoles. This is just one game that has excellent replay value and is fun for everyone from children to adults.
2 Golden Eye 007
Golden Eye was the best game in 1997, and to this day is arguably the best FPS to ever come out as it is the game that revolutionized the First Person genre. There is a lot more to do in this game than just blow away your enemy. Golden Eye 007 is built around 18 levels that must be played through in linear fashion in the easy mode, which will open up the possibility of playing the game in harder levels once completed. You will need to master all the different weapons available, as in some levels there are only a one or a few weapons available. You will also need to perform covert operations in typical Bond style all based on actual events from the Golden Eye movie. Just awesome.
3 Wave Race 64
Wave Race 64 features nine challenging water courses featuring buoys, ramps, mines, hairpin turns and more. You can compete in single races or in championship mode, which has three difficulty levels. The higher the difficulty level, the tougher the courses become and the more ruthless your opponents get. The challenge of the game is to race with the realistic water/wind physics inside the game (the first game to do something like this) and to also maintain max power the entire race - miss just one buoy or critical track section and you lose it and need to build it up again. Great water racing game.
Banjo-Kazooie is a platform game that features a goofy bear Banjo in tight yellow shorts who a carries a witty, red-crested bird friend Tooie in his backpack. Together, the bear-bird duo must use teamwork to complete various challenges and to rescue Banjo's sister Tootie from the ugly evil witch Gruntilda, who wants to steal her beauty. Bottles, a mole with Coke-bottle glasses, is around to assist where needed by teaching any new moves and on missions, you need to collect musical notes, Jiggys, Jinjos, Honeycomb and Mumbo tokens. Great family entertainment and a welcome change from the plumber :)
5 Pilot Wings 64
Pilot Wings 64 is a great flight sim where you choose a character and tackle flying assignments with various craft to gain your pilot wings. You are required to successfully complete challenges with a Hang Glider, Rocket Belt and Gyrocopter. If you make great scores during your challenges, you can open up bonus games. These include Sky Diving (Parachute), Birdman outfit (complete with wings and feathers), Jumble Hopper (huge bouncing device) and the human cannonball where you try to hit a distant bull's eye on a target. In my opinion, a game sadly over-looked and under rated, and in doing so, you are missing out on heaps of fun.
6 All-Star Baseball 2000
All-Star Baseball 2000 is a great baseball game that features 30 major league teams and stadiums in full detail. You can play the game in a variety of modes including exhibition, season and playoffs. The control mechanism of this game is where it really shines. You have excellent control over pitching, batting and fielding. The game also reacts slightly differently when game weather and surface conditions change and the CPU actually makes errors at random. This is my favorite cartridge-based baseball game.
As usual some of the top 6 list above is going to disagree with yours - I didn't include any Zelda titles in my Top 6 (though I'd rate Ocarina of Time in position 7 if I listed a top 10). We were fortunate that the Nintendo 64 had many good titles available, so here are some more that I recommend you play for this system: