Wild Arms 2 was one of the best RPG's I played for the PSOne. And it was one that not as many people either played or enjoyed as much as I did. But I stand by it to this day. The graphics may be very dated now a days, but the story, the characters(there's even a secret one) and the game play were near flawless.
I didn't see anyone mention Legend of Dragoon either. I was thrilled when they put that on the PSN. The idea of playing that game handheld was awesome! Yet another game that I remember almost everything about, to this day. Most of all, just for it's very addictive battle system. :)
I don't think it's on the PSN, but Valkyrie Profile was a game I played more than once as well. And it'll be a great day when they put Suikoden 2 on there.
And yeah, the basics, Everything the first person said as well as:
Final Fantasy 7 and 9. (didn't care for 8) And Final Fantasy Tactics
Breath of Fire 3 and 4. (both great games)
Man, this is making me want to put down the other stuff I'm playing to and jump into some old school games. :)