My favorites are Front Mission DS and Front Mission: Gun Hazard. I still have not played Front Mission 5: Scars of the War yet however, and it's considered the apex of the series by many vets.
How... how has Valkyrie Profile not been mentioned? One of my favorite RPGs ever on the PSX.
Honestly, the PSX and PS2 have the best stuff, it's definitely downhill as far as what's available on PS3. Ni No Kuni seems pretty decent from what I've played, but your mileage may vary. I also liked Eternal Sonata, I played on 360 but the games are very similar.
I'm sure I'll forget a few, but here's what I've played and enjoyed on PS1:
Valkyrie Profile SaGa Frontier 2 Vagrant Story Chrono Cross (terrible as a sequel, but a good game) FFVII (it's good, but it's not amazing) FFVIII (strangely my favorite on PSX) Arc the Lad 2 (seriously, it's friggin' awesome) Breath of Fire IV (Capcom. Bring this back.) Dragon Warrior VII (it's long, but it's good stuff once it's rolling) Grandia (definitely has the Lunar influence, but better) Legend of Dragoon (I liked it better than FFIX) Star Ocean 2 (fun stuff for sure, RIP tri-Ace (mobile company bought them out)) Suikoden I & II (best traditional RPGs on the system, probably) Parasite Eve (a bit of a proto-Vagrant Story in battle system, good stuff)
I also enjoyed Xenogears, the Tales games, Persona 2, a ton of those RPGs on the spreadsheet are good but flawed, and even the above can have issues.
As far as PS2...
Rogue Galaxy Dragon Quest VIII Shadow Hearts: Covenant Tales of the Abyss Valkyrie Profile 2 FFX Wild ARMs 5 Atelier Iris Arc the Lad: Twilight of the Spirits Grandia II (although I'd recommend the Dreamcast version instead) Growlanser Generations
And there's a TON more that's good, that I really haven't been able to sink a ton of time into. These are just ones that I've gone through that I considered worth mentioning.