Ultimate Spider-Man scratched a very similar itch to Spider-Man 2 if you ever want more of that kind of gameplay.

Not a PS2 game, but the PS1 Spiderman games are not to be slept on either.

Actually did not know this. Truly sad to hear it. Guess I can’t get rid of my dusty PS2 just yet

Some good ones that are not yet mentioned

• Ribbit King is Golf game with frogs for balls which get strategically shot around a map littered with bonuses and obstacles. Players alternate shots and try to have the most points after both players reach the hole. It’s extremely cute and great local multi-player fodder
• Stuntman is tough as nails. You are a Hollywood stuntman pulling off increasingly complex stunts for movies being filmed. At the end of each shoot you get to see the movie trailer filled with clips of your own driving.
• Black is a big dumb loud shooter, and it has zero reservations or shame in that. That’s what makes it so much fun to play
• Lord of the Rings: The Two Towers is excellent 3D brawling. Lord of the Rings: Return of the King is excellent 3D brawling with co-op
• Psi-Ops: The Mindgate Conspiracy is a 3rd person shooter where you have guns and psychic powers you use in and out of combat.