First, let me point out that the Gamecube was and still is the best system for this type of gaming. It just had a ton of releases for multi-player fun. Super Monkeyball was a nice surprise on that system with it’s variety of crazy mini-games.
Second, I’m going to suggest some of the genre’s we missed that are pretty much made for party gaming.
Dance games. I was a huge Dance Dance Revolution fan back back in the day day and I very much enjoy Dance Central and Just Dance this generation.
Trivia games. You Don’t Know Jack is the best for this, period.
Music/Rhythm games. People are really fond of Guitar Hero and Rock Band which are good for multi-player but we literally would not have those games with out the far superior Frequency. One of my favorite games on the PS2 and possibly of all time!