All PS2 games:
Klonoa 2
Sphinx and the cursed mummy
Choro Q game Series - ( Seek and Destroy, CHoro Q, Road Trip, Gadget Racers)- im an adult and still think they are the greatest/cutest racing games.
XGRA for a futuristic racing game. Wipeout might be a bit too difficult to enjoy it.
Jak X Combat Racing is a great futuristic combat racing game
Ratchet and clank
Bloody roar for a nice animal fighting game - sounds mature, but not really
digimon rumble arena
Dynasty warriors - any of them lol
any of the One Piece games are great multiplayer games.
s.l.a.i. - giant robot fighting
gundam battle assault - giant robot fighting
virtua on - giant robot fighting
RAD - giant robot fighting
Godzilla games - theres like 2 or 3 of them
Destroy all Monsters is great monster battles like godzilla
Rampage - monsters climbing on buildings and smashing them or eating people. repetitive but mindless fun.
Lego star wars
Burnout series ( the newer ones) - What kid doesnt like to race and smash cars and make big explosions?
Some of that list has already been mentioned, but I figured a double recommendation couldn't hurt ;P
All of them are really cheap now as well