WarpRattler's List of Recommended PS2 Games (note: he has not fully played some of these, but got a good enough impression from what he did play to suggest them; these games are marked with a single asterisk, and other people may want to give their opinions regarding them; also note that some of these games were also on the GameCube and you might already have/have had them so just ignore any of those suggestions if you do/did):
Katamari Damacy
Shadow of the Colossus*
Amplitude
Fantavision
Final Fantasy XII*
Dragon Quest VIII: Journey of the Cursed King**
Disgaea: Hour of Darkness***
Gradius V
R-TYPE Final
Soulcalibur II (or III)
Viewtiful Joe
Resident Evil 4
Xenosaga*
**Only if you want a hardcore JRPG.
***I've actually only played the DS version. Depending on how you view extras such as touchscreen control, portability, Etna Mode (also in Afternoon of Darkness, the PSP version), and bonus bosses compared with drawbacks such as the smaller screen, you may want that version instead of the PS2 version. Either way, though, it's a good game.
Please note that I'm not recommending any games, such as DDR, Guitar Hero, or Taiko Drum Master, that require extra peripheral(s), regardless of whether they come with the peripheral(s) or not - many of these games are rhythm games, so if you don't like those, you don't need to worry about that. I'm also not recommending Kingdom Hearts, though I agree with Lizard Dude that you'd probably like it because of the content.
