So being the Wild Arms arranger, sort of, I'm gonna recommend Wild Arms 1 and 3.
Wild Arms is western-style rpg with great story, battle system, music (OMG!), design, characters. It kind of feels similar to final fantasy games, the overworld, the towns, dungeons etc. But it's still very different and unique, more puzzely at times, kind of like Legend of Zelda. Few things are about the game is actually bad, I guess you could say it has aged badly being a ps1 game, kind of polygon-like. Also the bosses are very easy early on, but thankfully they get harder later on. I think it's available for PSstore or what ever the Playstation store is called, so it's just to go ahead and download. Finally I want to inform you of that they have also released a remake of the game for Ps2 called Alter Code F, with improved graphics and soundtrack, which looks really great!
Wild Arms 3
Now this game is even better. Having played the first, and being a solid game of it's own, this one just amazed me of the first impressions. Better graphics, being on Ps2, lot's of good unique stuff like the ability to move the camera around, looks really cool, ability to escape random encounters, obviously has the same soundtrack quality (Michiko Naruke is amazing), great dungeons. Fantastic game, all I have to say!
2 great RPGs I highly recommend to anyone who wants a new RPG. I haven't played the other games from the series but I've heard that Wild Arms 2 is kind of mediocre, and XF has some issues with the battle system.
2 other games that I don't think is that well-known, at least on this site:
Really satisfying racing game. You not only race against your opponents but you can also destroy them by making a Takedown. It's super fun, just mercilessly ramming your opponents and other cars around as you race to the finish. There are also other modes you'll play like Road Rage, where the goal is to do as many takedowns as possible, or Crash where the objective is to create a big car crash! I've played another Burnout game, Burnout Dominator, which way worse and due to only one thing: you couldn't ram neutral cars from behind, only your opponents obviously. This made it so you had to drive way more carefully and it really felt odd when the game seemed to be a game where you should drive recklessly. I don't know how most burnout games are, if you usually can shut cars from behind or not, but the fact that you can do so in Burnout Revenge makes it really fun to play!
Red Alert 3
Just a really fun strategy game. You play as Soviet, Allied or Japan, each having an own story mode. What makes the game so good is it's simplicity. You don't need lots of advanced strats in order to complete the missions, build a great army, destroy your opponent. Each country have their own cool weaponry, Allied got prism tanks, Soviet got Zeppelins, Japan got Onis (titan-like robots). It's a really fun and amusing strategy game all in all.