Kero Kero King - The predecessor of Ribbit King also known as FROLF. Its like golf with frogs but instead of getting the least amount of points like in a regular game of golf you have to score the most amount of points by interacting with objects scattered around the map within a limited number of turns. Its a lot of fun and has a great art style which is sadly missing in its sequel.
The Misadventures of Tron Bonne - This one isn't too obscure but I don't think many people know of this one despite it being in the Mega Man Legends series. Between Mega Man Legends 1 and 2 Capcom released this game, a prequel spin off about the character Tron Bonne and her Servbots and any game with a focus on Servbots is automatically a 10/10. It has the same proto cel shading look that the regular Mega Man Legends game has and still holds up so well visually.
Baroque - While this game isn't exclusive to PS1 as it also got a Saturn release I feel its still worth bringing attention to. Its an early roguelike where you continuously climb a tower and each run unlock more parts of the story. It has a great oppressing atmosphere with everything being rusty and dilapidated and really cool enemy design.
Skullmonkeys - This is a sequel to the point and click game The Neverhood. However, this game is a (sort of frustrating) 2D platformer and like its predecessor it is animated entirely with clay.