If you don't own this console, you're probably missing out on the best titles.
A little of everything.
The third Shin Megami Tensei game, localized without the III to minimize confusion, considered by most(myself included) to be the best SMT game of them all.
The third Devil Summoner game, detailing the adventures of Raidou Kuzunoha, ace Devil Summoning Detective, and the first real-time SMT action-RPG. Notable for having the most sadistic 'hard' mode in any game ever. The sequel is much better from a gameplay perspective, while the original has the better plot; subjectively speaking.
On the plus side, Raidou happens to know the best fusioner around.
And of course, one of the more successful and excellent stand-alone offshoot titles:
Digital Devil Saga: Avatar Tuner basically runs on SMT III's engine, but is a totally different beast.
Think Final Fantasy X's skill system + Nocturne's Press Turn + cannibalism + Hinduism with ambient guitar music and there you go.
There were a couple Persona games on the PS2 as well. I hear they're kinda popular.