Wow, I'm sure others have mentioned but 3 is really too small a number for the large amount of RPGs available to that console. So I'll cheat and use a few made up categories to recommend to you.
Dark/grittier RPGs (not horror or anything, but RPGs with a darker feel to them than the standard)
- Shadow Hearts 2. Recommend that you play 1 first, but 1 won't make it to this list. Very very fun overall, from the story to the gameplay to the references. Main character is definitely one of my favourites in any RPG.
- Shin Megami Tensei: Nocturne (post apocalyptic type of setting - very addictive demon fusion system and gameplay requires much thought)
- Shin Megami Tensei: Digital Devil Saga 1 and 2 - given together because it's no good playing them apart. 2 picks up where 1 deliberately leaves off.
Fantasy RPGs (the standard stuff)
- FF10, of course. Fun battle system, loved the sphere system and blitzball. However, hated the linearity (till I play 13...wtf) and the characters were a mix of annoying and alright. However, overall a good game, and its main villain was pretty awesome.
- Kingdom Hearts 2. Improved on everything that 1 was, and can be played without the first 1 if you really want to. You cannot own a PS2 / emulator without having tried KH2.
- Tales of the Abyss (great story, funny characters, fun gameplay..what's not to love?)
Something different, something interesting (games that do things differently, but were loved for it)
- Wild Arms 5 (although 3 is better, but quite standard JRPG so I can't put that here)
- Dark Cloud 2
- Xenosaga 3 (although 1 and 2 are good, but 3 is the best of the series in terms of welll...everything. Very lengthy game though, be prepared!)