bluejay

As someone who loves the PS1 but hates RPG games due to the addiction to fake achievement, I can recommend the following PS1 games so you can play more than GT 1 and 2 on the system:

- Abe's Oddysee, Abe's Exodus and Heart of Darkness: These 3 "Prince of Persia" style 2D games are beautiful, hard and generally awesome and fun.

- Driver: Very impressive for the PS1, great car handling and classic police series feel.

- Silent Hill: Fun gameplay, outstanding sound design and a story that you can't take seriously but with an amazing town to explore and huge immersion.

- GTA2: Hilarious radio stations with fake songs and fake DJs (including a parody Christian radio), fun gameplay. Saving a game is not simple, though: you have to save $50K and go to a church with a "Jesus Saves" sign. Antennas on TV vans, that you can steal, point to these churches.

- Goal Storm 97 and International Superstar Soccer Pro 98: I know you're American and you probably don't care about soccer. I also know FIFA 98 and International Superstar Soccer Pro Evolution were the 2 most acclaimed soccer titles for the PS1. But these 2 prequels of ISS Pro Evolution were actually better games: passing works better and the matches feel more like real matches. The controls are more responsive and less complicated.

- Croc, Jumping Flash! and Gex 3D: Everyone talks about Spyro and Crash, but these 3D platform games are very fun. Croc has tank controls and was described as "Tomb Raider for kids"!

- Tomb Raider: Everyone should play this game. It's the best on the series by far. The enemies are 99% crazy, wild animals and myhological creatures, the sceneries are gorgeous and mysterious and the exploration and 3D platforming is top notch. Later entries lost the magic adding more human enemies and using more boring stages with less exploration. (I recommend the MS DOS version because you can save anytime, PS1 has crystals)

- Destruction Derby 2: Crazy car game with only one downfall: you gotta drive perfectly or the IA will destroy you. Otherwise, fun gameplay with crazy metal music from the creators of Driver. Try to survive more than 1 minute in The Pit!

- Bust a Groove, Beatmania, Parappa the Rapper, UmJammer Lammy: The PS1 has a great arsenal of musical games. Beatmania is more serious and challenging, but the other 3 are really fun. You can also create your own songs with Music 2000.

You can also try Metal Gear Solid, Disruptor, Silent Bomber... and even Alundra, the PS1 version of Zelda! But I guess that's enough for today. I just wanted to point out that the PS1 has more than GT!

^Hell Yeah!  Plus Twisted Metal series and LUNAR games.

By the way @GoldLeader I tried Deadly Towers, and I can see why someone might like the game but I can also see why someone might call it the worst NES game.