Sabby may hate it, as it's a JRPG....
But there was a great PSX title from Sony called Legend of Dragoon.
Unfortunately, this game received VERY LITTLE advertisement, so it didn't sell very well in the US (at first. Ended up running 980,000 sold in the US). Several online critics like IGN rated the game pretty badly, while gamers did not seem to agree.
Another PSX title I adore is Valkyrie Profile. Unlike Legend of Dragoon, this game was highly rated by online critics, but it experienced a number of huge setbacks. A warehouse fire with a majority of the North American copies of the game caused a dramatic shortage, as did an issue with low-quality plastic media for the CD ROM discs (they tend to crack from the center of the disc). A used copy of Valkyrie Profile will set you back a fair bit of cash (and I wouldn't trust buying a used copy of a game online. I have made the mistake several times), and at minimum $300 US.
A possible alternative to shelling out hundreds on VP is to get the PSP port, Valkyrie Profile: Lenneth. Sadly, I do not own a PSP or I would have done this (as I used to own a copy of Valkyrie Profile, until the first disc cracked).
While it's a JRPG, it's very dissimilar to Final Fantasy and other JRPGs, using a more frantic and entertaining style of combat. The story and the characters are beautiful, the environments beautiful, and the side-scrolling action a nice change of pace from the traditional isometric RPG view.
The game has a LOT of replayability, with several endings based on your actions in the game. I don't recall if one is able to import old saves for a new game or not (I haven't played since 2001).