Legend of Legaia was a very good PS1 RPG. It was originally Japanese, and similar to FF (without being a clone), but it's in English, too, and shouldn't be incredibly hard to find. It was one of my favorite games as a kid, along with FFIX and Jade Cocoon.
Jade Cocoon is another great PS1 RPG, but I have a hard time judging whether it was actually amazing, or if it was just me. It's much more specialized, and I'm sure is not for everyone. It's in the monster-catching vein, but...different?
Both Legend of Legaia 2 and Jade Cocoon 2 were disappointing, but JC2 wasn't terrible.
EDIT: And I forgot to clarify, Jade Cocoon doesn't have
random encounters, but it has encounters. As in, the random enemies appear on the map and are possible to avoid (though not always).