Two words :
Fantavision (PS2). Period.
It\'s a crying shame so few people have actually even tried the game out by themselves, let alone with a friend. Simple, pretty, insanely competitive and also triggers bursts of spontaneous violence towards the opposing player, what more can you ask for?
Oh yeah, and a couple more "musts", both for PS1 (pretty rare nowadays, especially SPF2T) :
Bishi Bashi Special
Super Puzzle Fighter II Turbo
Both have all the attributes listed for Fantavision, except for the pretty factor. In BBS\'s case its ugliness is in fact one of its fortes.