Black if you're into FPS's
Sly Racoon (I've only played 1 but I've heard good things about the other 2) if you want something a bit different
Final Fantasy X if you want a damn good JRPG
Disgaea if you want a good story with some of my favourite characters on the PS2 (but don't get Disgaea 2)
Spiderman 2 if you want an amazing open world for a ps2 and the best web swinging action on any console
God Of War or God Of War 2, seriously if you like DMC you will like GoW and this is coming from a man who played DMV3 for 50 hours
Enter the Matrix: Path of Neo. Serious this game is so underrated, plays the story from the Matrix but makes them a lot more fun. Keeps key scenes and adds in new interesting ones, plus the combat is simple to use but takes time to master and get amazing with. If you can find this gem I would thoroughly recommend it
Finally if you are planning to get Ratchet and Clank, trust me getting Ratchet and Clank 2 & 3 are good choices too but do not get Ratchet and Clank: Gladiator, anyone who is a fan of the series will know why but 2 & 3 just improve on the original formula
Killer7 was a hell of a lot of fun but it is quite rare, if you can find a copy I would give it a try if you want a bit of mindless fun
If you are a fan of GTA then get Bully, another criminally underrated game
Star Wars Battefront 2, this game took so many hours just playing hour long matches against NPC's on various maps. Space fights, jedi and loads of maps to play, if you are a fan of star wars then it is essential, if you don't I would still recommend it because it has such good gameplay
Sorry for the epic post, I spent a good portion of my life with a ps2 and played a hell of a lot of games and most of yours among my favourite so I've had to dig deep within my collect to give you a good recommendation
Hope this helps