I, personally, really really like the Harry Potter games, except for Goblet of Fire. So...

I am so happy that someone agrees.
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Just so you know, guys, this topic is a month old. But, since more than one person replied, I'll recommend Kingdom Hearts 1, 2 and Chain of Memories, Ty the Tasmanian tiger(series), Sly Cooper(series), Harry Potter (series), Spyro: A Hero's Tail, Spyro: A New Beginning, Eternal Night, and Dawn of the Dragon, Tak: The power of juju, Tak: The Great juju Challenge,
  Tak: Staff of Dreams, Spongebob: Battle for Bikini Bottom, The Incredibles, Eragon, Nicktoons Unite, and the final fantasy games seem really really cool.

Okami is the best ps2 game I know! It was also a great hit on the ps2 logn ago (or so i've heard).

I was actually considering getting that game for wii at one point but after watching a few gameplay videos of it it just didn't appeal to me.

I know this must be stupid but The first 3 rachet and clank games are pretty good. It silly but very good it you like the guns stuff.

pretty good is an understatement I tried a couple of the ratchet and clank games and am completely hooked on them been playing them non stop since I got them.

I did get a couple other games jack and daxter barely tried it, ty the tasmanian tiger, I did get the 3rd 1 but it doesn't work on the silver ps2 also gran turismo 3 and 4 since i love racing games.

Shadow of the Collosus (a MUST have)

ummmmm i dont have a single E game.....

Final Fantasy X, XII (T)

Thats about all the suggestions i can give u.

~Harry Potter Chamber of Secrets- you run around Hogwarts and do really fun stuff and get like Tasks. funn.

~Harry Potter Prisoner of Azkaban - same thing.

~Grand Theft Auto San Andreas - You get missions but your basically in a gang and you get to just go around and kill people Sticking out Tongue

~Dance Dance Revolution {with the dance mat} - simple, its the dance mat game thingy

~The Sims 2 - Not as good as for PC but still fun. And you can play with 2 people. Laugh

~Harvest Moon: A Wonderful Life 'Special Edition' - suchh an addicting game I love it. You are a farmer and you get to raise animals, fish, grow crops, and do other stuff.

~Guitar Hero - Self explanatory I hope you know what that is. When you have the guitar and you rock out haha.

I don't know I have a LOT of games for ps2 but I am blanking.

I would advise more, but I'm on limited time. These are some of the best.

-Soulcalibur 3 (combat , good challenger of Tekken as everybody say , but I haven't got any recents Tekken , so...)

-TimeSplitters Future Perfect (if you don't have friends (happens sometimes) and dislike FPS games , don't even try this game , he will not last long without the multiplayer mode...and it's a pure FPS games with funny features inside...but not for all publics maybe)

-the last Legend of Spyro game , Dawn of the Dragon (no comment...see the forum for more precisions about this game...) , I haven't found the others of the series (our video games shops sucks in occasions) so I don't know if they are better

-Metal Gear Solid 2 and 3 , because they are monumental games , but that's not the type of game everybody bear (infiltration games) .I really like both of them (and there's no problem' if like me you skip the number one on PS1 , he is so rare that I can't even find one...)

-Jak or Ratchet , you are going to have a hard time choose between the two...do like me , take all the games of the two series , PS2 aren't expensive at all today  :-P  (platform games)

-Mindnight Club 3 remix (remix is even better than the original) , (but it's an arcade car game , not a simulation...)

the others game I own and would avise to you are already said , so now , choose between the big choice we let to you

EDIT : I have failed...
I forget one of the single better games ever in PS2 (and the favorite of the Japanese) (please forgive me fans of this game :-[ ) : Final Fantasy 10 (I wonder what nobody think of this game before me) , one of the best RPG ever , ever , go buy it and play it NOW...okay , sorry , but it's THE game you HAVE to try on PS2 if you really enjoy RPG games , trust me , there are enough fans of this game to show it (Japanese around here ??) (and there is also parody of it , the better games of the PS2 have all their own parody you know ???