I personally share your opinion in that sports games are not my thing. I obtained a ps2 about three years ago, and in that time there have been less than 30 games, so it should be quite easy to pick from that selection.
1.Tales of the Abyss -
The last Tales of
game to be released on the ps2 has, arguably, a better battle system than all it's 3D predecessors.
2.Star Wars Battlefront II - A third(or first)-person team shooter
with a star wars theme which works suprisingly well and is loads of fun. There are still people who play online, the most enjoyable part, but lately there has been a glitch which renders it inaccessable.
3.Shadow of the Colossus
- This is an action game involving a massive expanse of wilderness, almost no dialogue, and sixteen (could possibly have been 22
) boss battles. Other than shooting fruit off trees or killing lizards, they are the only enemies.
4.Mega Man X Collection - Mega Man X, X2,X3,X4, X5, X6, and a racing game on one disk. X2 is my personal favorite.
5.Spider-man 2 - There is always something to do. The city is full of events, people in need, and buildings on which to swing/crawl/leap from/play on.
6.Ace Combat 5 - The Unsung War - Jets shoot things. That's all that needs be said really.
7.Kingdom Hearts II - A combination Disney and Final Fantasy action rpg and rail shooter.
8.Disgaea - Hour of Darkness - A tactical jrpg with a humorous spin. When I first heard of this game and it's premise "demon prince sets out to establish himself as ruler of hell" the image that came to mind was an action game featuring a demonic, completely black specter-like ragged humanoid with horns and glowing orange eyes, luminous orangish misty breath, a sword, and tattered clothing fighting hordes of monstrous hostile enemies with style atop a high ridge on the edge of a massive cave with magma in the abyss. O_o man was I surprised. Turns out my imagination had more in common with devil may cry(which i had never heard of or seen at the time), eh?
8.Viewtiful Joe - A unique sidescrolling beat-em-up where you are pulled into a superhero film's universe and have access to director abilities such as slow motion and fast forward.
9.Psychonauts - Funny, cool, neat, and fun in exploring psyches and a campground.
10.Soul Calibur III - A fighting game with weapons.
The later ones seem bereft, but that's because this post has taken me over an hour and a half to compose.