Ape Escape was mentioned. That game was released to promote the dual analog controller on Playstation 1. Back then the convention of camera control on right stick wasn't even established, so camera rotation was on the shoulder buttnos, while the right stick was used to control weapons!
The game's soundtrack is iconic. Dark Ruins is a favorite: https://www.youtube.com/watch?v=1jbNHgmU1TM