Don't forget Tony Hawk Pro Skater. Where the legacy began. Arguably the best in the series.

Hard Edge
Tobal No. 1
Rollcage
Gunners Heaven
Jade Cocoon
Rhapsody A Musical Adventure
Einhänder
Alundra
Alundra 2
Tales of Destiny
Grandia
Brave Fencer Musashi
Star Ocean
Valkyrie Profile
Xenogears
Wild Arms
Wild Arms 2
Legend of Dragoon
Breath of Fire III
Breath of Fire IV
Chrono Cross
Parasite Eve
Parasite Eve II
Mega Man Legends
Mega Man Legends 2

Fixed. S̶i̶n̶c̶e̶ ̶t̶h̶e̶ ̶g̶a̶m̶e̶ ̶w̶a̶s̶ ̶n̶e̶v̶e̶r̶ ̶r̶e̶l̶e̶a̶s̶e̶d̶ ̶i̶n̶ ̶E̶u̶r̶o̶p̶i̶t̶'̶s̶ ̶v̶e̶r̶y̶ ̶u̶n̶l̶i̶k̶e̶l̶y̶ ̶t̶h̶a̶t̶ ̶t̶h̶e̶ ̶O̶P̶ ̶c̶a̶n̶ ̶f̶i̶n̶d̶ ̶i̶t̶ ̶i̶n̶ ̶a̶ ̶l̶o̶c̶a̶l̶ ̶s̶t̶o̶r̶e̶. According to ebay, the cheapest used copy is close to €60, which is pretty expensive for such an old game. Not sure if the OP has any luck with a local store.

Edit: Whoops. Fixed my mistaken assumption.

The only PS1 games I still own (mint if it matters) are FF7, FF8, FF9 and Metal Gear.
Fun fact. Metal Gear was remade on the Game Cube and titled Twin Snakes. It plays similar to Sons of Liberty which is a huge improvement over the original PS1 version.

SaGa Frontier is a very good non-conventional RPG that takes place in a setting containing both robots and magic (both accessible to the player). You get 7 characters to choose from (but don't choose Lute on your first playthrough).

SaGa Fronter 2 is a very good non-conventional RPG that takes place in a common magic medieval setting and whose plot spans over 80 years.

Note that these two games are quite different from one another; therefore, if you (don't) like one of them, you won't necessarily (not) like the other.

Enhander
way of the samurai
tenchu 1
warzone 2100
tiny tank
spiro 1
spiro riptos rage
gex all of them the 3d ones

gundam battle assault

These are pretty damn cool games I grew up with and are solid for short bursts and long play time.

Tomba 1&2, although you're looking at a considerable outlay if you're trying to collect these things in mint condition.

I dub this list "The Deep Pockets Collection". All you're missing is Lunar 1 + 2. :P

Dude tomba 1 was my jam back in the days and now it goes for almost 100 -_-

I should mention that I'm not looking for mint games, I just want to play them and enjoy them lol.

More:

Sol Divide
Alien Trilogy
Forsaken
Disruptor
Fighting Force
The Raiden Project
Theme Hospital
Dino Crisis 2
Tenchu II
Builder's Block
Bomberman Fantasy Race
Chrono Cross
Cool Boarders 3
Einhander
Crusader: No Remorse
Tail Concerto
MDK
Rival Schools

I'm gonna back everyone that mentioned these games in particular:

FF Tactics. (The original, despite the translation "issues" is just so much better than the War of the Lions version.)
Bushido Blade 1 and 2
Castlevania: SotN
Blood Omen: Legacy of Kain
Alundra
Diablo 1 (Yep, there was a PS1 version.)
Tactics Ogre
Ogre Battle
Front Mission
Dino Crisis
RE Trilogy
Medieval
Parasite Eve 1 + 2
Tekken 1-3
Street Fighter Alpha 1-3
Time Crisis (If you get the Guncon and have a TV that still supports it.)
Brave Fencer Musashi
Silent Hill

Honestly, you can't really go wrong with a lot of the RPGs mentioned in this thread or on the PS1 in general. I'd consider that particular console generation as the golden age of RPG/JRPGs.

I thought the OP wasn't interested in obvious must-have games, like Silent Hill and Resident Evil(s).
Otherwise my list would've been much bigger.

you must try vagrant story! then there is also vagrant story and ... oh did i mention vagrant story already?

there are a lot of great games, like star ocean 2, suikoden 1 and 2, sheep raider, kings field 1, 2 and 3, shadow tower, alien resurrecton, hellnight, ff tactics, ogre battle ...

tenchu 1 and 2, fear effect 1 and 2, parasite eve 1 and 2, ...