Well... the horse owns every Mario Party except 3, which the girls that lived across the hall from him rented for quite some time during the Horse's freshman year of college.
Anywho, MP1 I played mostly with my dad and brothers, it was fairly repetitive, and it was always a coin toss if you got the star or Bowser if I remember correctly. It did have the most boards though, so that's gotta count for something.
MP2 was a big hit in my dorm for whatever reason, I think it was because the girls could play too.
MP3 was really an upgrade from 2, but a lot of people didn't play that game, since it came out near the end of the n64's existance, and I believe after the ps2 had appeared.
MP4 isn't bad, although a lot of the boards were quite similiar.
MP5 was sad because the monkey (my beloved monkey the only character I had ever used) was no longer a playable character, so it loses points for that, but gets them back for the variety of event spaces. Plus that was the game my ex girlfriend liked to play with me.
MP6 I've had since X-mas, but it still sits in the box, unplayed so far, I'm looking forward to giving it a whirl though... soon.
Horse's ratings (not including 6 until I open and play it):
1. Mario Party 3
2. MP 5
3. MP 4
4. MP 2
5. MP 1