People talking about their poor hands always gets me with Mario Party - I weep for the fragile N64 control sticks before people's self-abuse.
Split controller mode in MP7 is pretty awesome though if you have people really into it. I played a game recently and it was this awesome strategic mess. Being able to choose who represents the team in some minigames led to some hilarious "oh, you can play this minigame because I know you can take the other guy" discussions.
I thought MPA was actually pretty cool, obviously it's not much of a multiplayer game but the main mode has a really weird charm to it. I actually printed off and laminated the physical board that originally came with it and played it with people. There's a selection of 10 or so "Gaddget minigames" where you all share a GBA/controller. It's has some funny upsets where people get sent back to the start, but most of those minigames barely qualify as minigames and get repetitive and it's literally 100% luck based without much depth. It's a shame there wasn't more to that mode or actual in-game link-up gameplay.
I also picked up Mario Party-e recently and it's alright, but the e-Reader card-scanning is more of a hassle than its worth.