My favorite Mario Party is 2. It's the one our family plays all the time, the mini games are fun, the maps are great. We just have a whole lot of memories with it. My favorite map is hands down Western land. I don't know if it's the music or the style of the place, but it always just stood out to me more so than the rest.
My favorite mini game in 2 is hexagon heat, oh goodness we have so much fun with that. In order here is my favorite to less favorite Mario Party titles.
Favorite - 2,3,4,10,6,5,7 and 1 - less favorite
1 feels weird and the mini games are just off, the maps are still fun though, but it's also my least played Mario Party.