IIIIITHE1IIIII on 25 March 2015
For me it's a tie between Mario Party 3 and 5. Both have excellent mini-games, 3 has excellent boards (including the unique dueling mode) while 5 has excellent bonus modes (ice hockey in particular).
The first and second entries feel undeveloped, 4 feels rushed (lower mini-game quality and quantity than Mario Party 3), while my experience with 6/7 is too limited to have a fair opinion. I have many fond memories of 7 though, so if I ever owned it I'm sure it would have been a contender.
Never played 8 or 9, but I'm considering buying 10.
