Dead or Alive: although it is over sexualized, it is a surprisingly deep 3D fighter (hehe innuendos)
Project Snowblind: it was a futuristic shooter set in 2100(?) Hong Kong that was released for PS2 back in 2005 (an eidos game I believe). I beat it quite a few times. It was a good game!
Theme Hospital: loads of hospital sim fun
Age of Empires: very fun back in the early 2000's, especially with the photon man and big daddy cheats lmao
Twisted Metal: pure fun. I played TM2 so much with friends and family. Just like Rocket League found out, using cars in different scenarios can result in great games