Snowboard Kids 1 and 2.

Phew... many to name.

Bomberman 64, Rayman 2, Snowboard Kids, Mischief Makers, Rogue Squadron, Turok 2,
(Beetle Adventure Racing)

quest 64, ogre battle 64, mischeif makers, the wrestling games on n64 were great also

I think I'd go with Spider-Man, unless I'm missing something critical. Resident Evil 2 deserves a mention for how impressive the port is though.

Two of you beat me to it, Quest 64.

Mystical Ninja Starring Goemon

It was Zelda, before there was a Zelda on the 64. It had pretty cool in game cut-scenes and overall was a robust experience early in the 64's life cycle.

As a runner up, I'd go with Mega Man 64. Love the simple art style and although the gameplay was a bit janky, it was still fun to control Mega Man.

Rayman 2 but I´ve never played Turok 1 and 2, Duke Nukem 64, Bomberman 64, Rogue squadron or Mystical Ninja starring Goemon.

One of the first games I´ve ever played and is one of my favorites of all time. It left such an impression on me that I bought everything rayman related I could find. It was an amazing experience and Im super glad that one of my first gaming experiences was with a masterpiece like this one. 

Excitebike 64 -- published by Nintendo but developed by Left Field Productions.

If that doesn't count, probably Rogue Squadron or Turok.

There are quite a few really good non-Nintendo or Rare games on the N64.

The biggest problems are outside of a few many of them are rated M or licensed games.

Most have already mentioned the really good ones, I will say that Winback: Covert Operation was great and did cover based shooting before Gears of War made it cool. Also Wetrix is one of the best puzzle games it seems no one got to play. I enjoy many hours with that game on the N64.

I really enjoyed Hybrid Heaven.. finished it 100% and even maxed out my character in the MP mode.

Cant think of my none Nintendo/Rare favourite N64 title, there was a lot of very good games.

Maybe Turok 2