I've got a handful to list off.
Ghoul Panic
Similar to Point Blank, this is a series of light-gun challenges involving shooting targets. The difference was here you had to shoot ghosts to stop an evil witch. It was only released in Japan and Europe.
Namco Anthology 1 and 2
The lesser known PS1 compilations of Namco arcade games, certainly because they were Japan-only. Unlike the Museum games, these had a website aesthetic, and each game also included a remaster. The Pac-Attack revamp should look very familiar to Pac-Man World 2 players.
Ore No Ryouri
A cooking game which prioritized the use of the analog sticks. It's probably best known for inspiring what would become the Cook, Serve, Delicious series.
Bishi Bashi Special
A series of arcade games focused on puzzle and skill minigames. The PS1 had several ports of the games, including 2 which were packed onto a European release.
Bust a Groove 1 and 2
Despite jump-starting the genre, the PS1's line-up of rhythm games tends to get ignored outside of Parappa the Rapper and kin. Here was a competitive dancing series which featured a great and varied soundtrack. Difficult, but a lot of fun.
Rhythm N Face
Another rhythm game, this time by Osamu Sato, best known for games like LSD: Dream Emulator and Eastern Mind: The Lost Souls of Tong Nou. Here, you would create pictures of faces with squares, circles, and triangles. It even had
an art book.
Playstation Underground
A quarterly magazine which consisted of two CDs: one with videos about upcoming games, PS1 hardware, etc., and one with demos. It lasted for 17 issues until it merged with Official U.S. Playstation Magazine, shortly after the PS2 launched.