The Jak and Daxter series, along with the Ratchet and Clank series. Be sure to check out some of the cool Nick Games like Tak and the Power of Juju, and Spongebob: Battle for Bikini Bottom. I would also recommend the Spyro series, since that iconic purple dragon is awesome. There's also the Sly Cooper series, and the GTA series. My list goes on, but those are the top PS2 games.
surpised no one has said any of the 「King of Fighters games, Silent Hill 3 & 4, Metal Gear Solid 3, Shadow of the Colossus, Resident Evil 4, Hitman series」 ←All top rated games
Of course everyone has a second chance, it's called tomorrow.
Silent Hill 2, 3, and 4. Face it, Silent Hill 2 was great because it failed so much. Have you ever made fun of a game like that before? Final Fantasy X, X-2 [Just for closure on X] and XII. XII doesn't get the attention it deserves. Definitely get Gauntlet: Dark Legacy. Now my personal favourate is Klonoa 2 but that one will run you a good $30-50.