Lets try and keep this thread less like a list and more discussion focused. Not to say you shouldn't make a list, but try to discuss said lists.
I'll kick it off with a few of my favorites...
Sly Cooper, Tekken, Soul Calibur, Dragon Ball Z: Budokai Tenkachi.
I would recommend Tenkachi to anyone, even if you despise everything about DBZ. http://www.youtube.com/watch?v=CUL_J-sig1A video should speak for itself. The most fun I've ever had with a fighting game (I've played a lot of fighting games), deep character customization, and over 250 unlockable characters.