Games that I'm confident the average person would love:

• Burnout (3 and/or Revenge)
• Tony Hawk's Underground (definitely 1 and not 2)
• Shadow of the Colossus (I'm otherwise avoiding games with HD versions for modern platforms but I specifically think this game is weirdly better with PS2-level graphics and performance)
• Ultimate Spider-Man (Spider-Man 2 had better swinging but I think this is the stronger overall package)

Games with a more niche appeal but, dammit, I want you to play them anyways:

• Steambot Chronicles
• Shadow of Destiny

Games that felt like a big deal at the time but I haven't actually played since I was a kid so take with a grain of salt:

• Evergrace
• Way of the Samurai (1 and/or 2)
• Stuntman
• Def Jam Vendetta & Fight for NY
• Mercenaries 1
• NBA Street (2 was my favorite but all three were great)
• NFL Street (only played 1, presumably 2 and 3 are also great)

A game I know is bad but I want you to play it so that the voice clips will be burned into your brain also:

• Kessen 2