Let me look
Alundra - Basically Legend of Zelda: A Link to the Past on PS1
MDK - One of the only good 3rd person shooters ever made. A Lot of fierce debates over where MDK or MDK2 (Shiny vs Bioware) is the better game
Mr Driller - Not filled with all the variants and sidemodes that Drill:Land has, but the core-gameplay loop of one of the greatest arcade-puzzle games is already in place. The final challenge of getting to 2000M is pretty tough.
Devil Dice - Brilliant Puzzle Game. I've only played the PS2 sequel Bombastastic though
Colony Wars + Colony Wars: Vengeance - These are somewhat lightweight but fast paced 6 Degree of Freedom space games. The genre namesake (Descent) is based on flying through caves instead of open space so they feel very diferent in that regard. Recomendation is mostly because of atmosphere. The 2nd game's story tries to convince you that the 1st game's story was propaganda all along.
Crash Team Racing - Stages are better than essentially any Mario Kart... but the in-depth drifting mecahnics means that this is almost Mario Party 1 levels of hurting your real-life hands
Ape Escape 1&2 - The best 3D platformer of PS1. Can feel short if you don't have a completetionist attitude because you don't NEED all monkeys in a level (but mario doesn't need all stars in a level either tbh). I think the 1st game is mostly better, but 2 does have a wrestler that suplexes dinosaurs in it.
Tony Hawk's Pro Skateboarding 1&2 - some of the greatest game's of all time.
RPGs - Grandia 1, Final Fantasy 7, Front Mission 3, Vagrant Story. ---- ALL 4 of these games have some annoying qualities that prevent me from using them as general recomendations - Also any of them are 4 times the time investment of other genres, this being PS1.
Grandia 1 has 2 appeals = the unique timeline battle system, and the "childhood wonder" story theme it has for disc 1. Technically Granida 2 and espeically the recent indie Child of Light can showcase the timeline battle system with a ton less playtime, but I just really didn't like the charathers/world in them.
Final Fantasy 7 - I like this game because it has themes of vulnerability and false idenities. This game also breaks up tension with humor which I feel like is really rare for PS1 even though SNES RPGs did it all the time. I feel like it has much better pacing than most FF games, although it doesn't quite get into Chrono Trigger / Dragon Quest (Hustle you along) territory.
Front Mission 3 - I consider it the best PS1 SRPG > FFT and Tactics:Ogre. This is mostly due to problems with bloat in the latter two games. Although FM3's mecha theme and superior music certinaly help.
Vagrant Story - A single charather RPG that is kind of a 3rd person action game but has you use a psuedo turn based thing for individal sword swings (without leaving the overworld). After the 2nd~ area equipment and level up skill choice can become extremely important and many players quit in frustation from doing single digit damage. I feel like it's a great game but I don't recomend it much because of this.