If you're not opposed to fully 3D platformers (starring cute kitty and dog people), I highly recommend Tail Concerto.
I'm definitely not opposed to them, and I actually picked this up recently, although I've yet to play it. I got it and Kaze no Klonoa together for like $13. My PS2 is on the main TV, which the wife occupies most of the time. I'll try it out soon though.
On the RPG side of things, definitely pick up Valkyrie Profile if you haven't already.
I have not, but was thinking of nabbing this before I leave. It seems to be quite popular.
I could name a lot of other worthwhile PSX titles
I've picked up quite a few that were listed towards the top of the thread, so feel free to make some more recommendations.