I've actually played these in the GameCube era (2002-2007), but anyways, here's my list (Comments are in brackets):
5. Diddy Kong Racing [Loved how different it was from MK64]
4. Super Mario 64 [Exploring was cool, but using the Wing Cap was awesome]
3. Rolly Robot [I believe that's what it's called; loved the custom roller coaster]
2. Iggy's Reckin' Balls [Loved the destruction whenever I got 1st place]
1. Mario Party 3 [Being able to play as Peach was fun]
Here's a runner up, because I felt I had to include it (Don't worry, the title isn't strict):
* Mario Kart 64 [The desert track was my favorite; couldn't get enough of the steam train]