The PSX is a RPG paradise. Unfortunately though, a lot of games I propose won't be $10-20.
Here's a list of my own PSX games, with very short descriptions of each game.
Arc the Lad Collection- To me, it was well-worth the $70, but EB has it for $50 now. three awesome Strategy RPGs
Azure Dreams- you travel into a huge randomly generated tower with monster companions. there's some dating sim elements too
Brave Fencer Musashi- quirky little action/RPG by Square. I still haven't finished it though.
Breath of Fire III- solid RPG, similar to the SNES BoFs
Breath of Fire IV- in the process of playing, its good
Bust-A-Move 4- good puzzle game, but its a little too easy, and you get ridiculous combos for no apparent reason
Chocobo's Dungeon 2- eh, its kinda boring. Ultros is indeed a boss in it though
Chrono Cross- if you don't start playing it expecting another CT, it can be decent. too many characters
Dragon Warrior VII- I'm 90 hours into this game with a lot to go. very long, but if you like DW, you'll love every minute of it
Ehgeiz- it sucks
Eternal Eyes- bought it for $7, and haven't really played it yet
Final Fantasy VII- I'm sure there's tons of people who'll disagree, but this game kicks ass.
Final Fantasy VIII- I have problems with the story and gameplay, but its still a good game.
Final Fantasy IX- probably the best of the PSX FFs. must buy
Final Fantasy Anthology- FF5 & FF6 with slow loading times, and a four CG sequences. You must own FF6 in some form though.
Final Fantasy Chronicles- FF4 hardtype & Chrono Trigger. Only Chrono Trigger's loading times are bad, but they added anime cutscenes.
Final Fantasy Origins- very nice port of the WonderSwan remakes of FF1 & FF2. no bad loading times at all.
Final Fantasy Tactics- my favorite Strategy/RPG. extremely addicting Job System
Front Mission 3- mech Strategy/RPG by Square. Its pretty good, and very long
Grandia- some say its drags on a bit, but I really loved every minute of the game. An epic RPG
Legend of Dragoon- haven't played it
Legend of Legaia- fighting system was pretty cool. decent story as well
Legend of Mana- very different from SoM. The game is mission based, with no major storyline. I liked it, but a lot of people don't
LUNAR:SSSC- a classic. almost my favorite game on the system.
LUNAR 2:EB- very good, most people like it as much as the first
Mega Man 8- its usually dirt cheap, and it a traditional Mega Man game.
Mega Man Legends- at the time it came out I liked it, but I can't see playing it again
Mega Man Legends 2-haven't really touched it yet
Misadventures of Tron Bonne- its short and easy, but it was enjoyable
Parasite Eve- haven't touched it yet
Persona- these games have a cult following, but I didn't really get into this game. I want to replay it.
Rival Schools- awesome fighter, with a lot of great characters.
Rhapsody- this RPG is hilarious. characters will burst out into singing at times. I love it. Very easy though.
RPG Maker- it totally sucks. no keyboard. PC version is so much better
Saga Frontier- I liked this game a lot. very unlinear. you play the story of multiple characters.
Saga Frontier 2- I got stuck in this game. I need to replay it.
Saiyuki: Journey West- Strategy/RPG with a good storyline.
Shadow Madness- haven't really played it much
Star Ocean 2- Awesome game. Awesome battle system. Tons of custimization, and building items
Suikoden- another classic RPG. 108 characters, gripping story. A little short though.
Suikoden II- better than the first. borrows a lot of the gameplay elements, but is easily twice as long and has a much better story.
Tales of Destiny- Great RPG, with a great battle system similar to a 2D fighting game. Great storyline as well.
Tales of Destiny II- supposed to be called "Tales of Eternia". Its still has the kick-ass fighting system, and rules in all other areas.
Thousand Arms- a Dating Sim/RPG. you have to date chicks to get spell. Its hilarious, and actually a solid RPG.
Torneko:The Last Hope- an RPG/Dungeon crawler. if you're a masochist, you'll love it. extremely hard.
Um Jammer Lammy- the sequel to Pa Rappa da Rappa. very catchy songs
Vandal Hearts- short Strategy/RPG. ridiculously gory. decent.
Vandal Hearts II- improves on every aspect of the first one. much harder, longer, and better.
Vanguard Bandits- a good Strategy RPG. hilarious translation by Working Designs
Vagrant Story- Action/RPG very deep weapon/spell system. very hard.
Wild Arms- a good RPG with some good puzzles.
Wild Arms 2- its in 3D, and worse than Wild Arms 1.
Xenogears- very long, but its story is pretty amazing. its also hard at times, and very text-heavy