If violence were up for consideration, I'd suggest Ratchet: Deadlocked. It's a Ratchet & Clank game focused on combat more than platforming, but it's a load of fun and has a lot of hilarious narration.
If PS1 games were up for consideration, I'd say Crash Team Racing because it's the best kart racing game for PS1 in my opinion. Crash Nitro Kart is a solid clone of it for PS2 but I didn't think it had the same charm as the original.
Timesplitters 1 2 3
All fun FPS and the best multiplayer of any FPS ever.
Red Dead Revolver
A fun TPS with many different characters (most must be unlocked in story mode).
Gauntlet Dark Legacy
An hack and slash/rpg game with many levels, has 4 player co-op.
Star Wars Battlefront 2
Its pretty fun.
Tekken Tag Tournament
This game is unique because you can play 2 player co-op in a fighting game. This is IMO one of the best fighting games ever.