I have that for the Gameboy Adv. Even though on the GBA it's a Fire emblem clone, it's still super-fun to play.
I recommend Marvel: Rise of the Imperfects, Ultimate Spiderman, MGS 2 and 3, Transformers Armada, Battlefront 1 and 2, GTA: Vice City and San Andreas.
Yeah, there are a ton of Shin Megami Tensei games out on the PS2. Persona 3 an 4, Digital Devil Saga 1 and 2, Nocturne, and Devil Summoner 1 and 2.
Check out Gamefaqs lists and its always fun googling for good obscure games. Soooo many gems for ps2.