Most JRPGs I have...examples being Kingdom Hearts 2, Crisis Core, FF IV, Fire Emblem Sacred Stones. Those are in fact the only ones I can think of...
As for Shooters it's:
Battlefront 2 and Battlefront Renegade Squardron, Medal of Honor Heroes, Halo 3 [when I play it with my cousin]
1-on-1 fighters is probably Soul Calibur 2, Talim takes the cake.
Side-scroller: Prince of Persia Fallen King for the DS. Best controls ever, it's just when they pulled out the enemies that blocked every attack on both sides of me with no checkpoint before it, then I couldn't go on.