Depends on what you like.
Maybe fighers? Tekken has been mentioned, maybe Mortal Combat.
Timesplitters (also mentioned) is a lot of fun, supports up to four players.
I am trying to think of any good racing games, but the only one I liked was Burnout3 and that does not have split screen IIRC.
“The only way to deal with an unfree world is to become so absolutely free that your very existence is an act of rebellion.”
- Albert Camus