Tenchu Is a must, it was the first real stealth game I played.

What kind of games do you like.  Are you open to all suggestions?  

Brave Fencer Musashi and Legend of Mana.  You're a fan of Kingdom Hearts so you'll probably like these action/adventure action/RPG games.  Brave Fencer Musashi has one weapon that levels up in attack power as you use it, otherwise it's similar to Zelda except with a lot of platforming, your character can absorb enemies with one sword to use the abilities to solve puzzles, and your character gains new attacks combinations when attacking in different combinations with both weapons.  Legend of Mana has multiple different weapon types, and it's got a pretty combo heavy system despite using one button for attack and two other buttons for extra skills.  While you use one button, there are attacks that are timed or directional based while attacking, using different skills like roll, back flip, jump, etc, you'll do additional attacks like an upwards kick as you do a backflip, or a downward slash.  A detailed weapon and magic upgrade system, plus monster taming and robot upgrade system. 

Twisted Metal 2.  Shows you have Twisted Metal 4, and TM2 is the best one on the PSX. 

Brigandine, Arc the Lad 2, and Tactics Ogre LUCT.  The  three best TRPGs in my opinion, fourth is FFT.  Out of all games, not just the PSX library.  Brigandine has six different countries to start as, and has infinite replay value.  Tactics Ogre is around 60 hours and has three different story arcs which change the storyline pretty drastically during the middle chapters.  Arc the Lad 2 is part of Arc the Lad Collection which consists of Arc the Lad 1, 2, 3, and Arc Arena.  So around 80 hours of content if you just plan to finish the three  games without doing any of the side content or any Arc Arena content(the first game is less than 10 hours.)

Other very good TRPGs.  Front Mission 3 has you upugrading Wanzers as you progress through one of the games two 30 -40hour campaigns.  Based on what you answer at the very beginning, whether you choose one option or another, the game is completely different both in battles you'll fight and the storyline(it's like playing two completely different games with the same gameplay and main character.)  Vandal Hearts is similar to but better than Fire Emblem in every way imo. 

For regular RPGs.  Wild ARMs 1 and 2, Breath of Fire 3 and 4, Grandia, Legend of Legaia, Suikoden 1 and 2, Star Ocean 2, and SaGa Frontier.

Rogue like RPGs.  Azure Dreams, Chocobo's Dungeon, Torneko the Last Hope.  Azure Dreams is the best of these, but the other two are great games.

For non RPGs  that are overhead games similar in style to Zelda, there's Alundra and Blood Omen Legacy of Kain.  

Other games I'd recommend  are Omega Boost, Die Hard Trilogy, Driver, Castlevania Symphony of the Night, Nightmare Creatures, Mega Man X4, and Syndicate Wars.

There are other recommendations I'd give, but these are the more highly recommended games.

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Dude! How could you forget about legend of dragoon?

Please please please, track down a copy of Tomba! 2. They have an English version.

Digimon World 2 was surprisingly addictive too, and a ps1 exclusive, probably as a counter to pokemon and Nintendo

Einhander is a good one.