The PS1 has a good library; as most others have said, though, it's aged extremely poorly. The polygon models are extremely simplistic, and the textures have that "shifty" effect that just looks bizarre. N64 games have aged better thanks to their crisper look, but not by much. Still, there's some fun to be had with the system.
My favorites, in rough order from most to least:
Blood Omen: Legacy of Kain (An amazing 2D Zelda-like... if you can stand the loading times)
Fear Effect 1 & 2 (You've probably never heard of these, but if you like Resident Evil or Metal Gear Solid, you owe it to yourself to find them)
Silent Hill (Still the best of the series in terms of scares)
Persona 1 & 2 (Addictive dungeon-crawling RPGs)
Metal Gear Solid (Duh)
Legacy of Kain: Soul Reaver (Only if you can't play it on the Dreamcast)
Resident Evil 3 (The best of the "classic" RE's, in my opinion)
Grandia (Perhaps the most fun JRPG combat system I've ever had the pleasure of playing)
Legend of Dragoon (Better than any PS1 Final Fantasy game, but with the most horrible [and unintentionally hilarious] localization I've ever seen outside of Zero Wing.)
Parasite Eve (Survival horror with RPG elements and a fun/cheesy-as-hell story)
Dino Crisis 1 & 2 (Resident Evil with dinosaurs. What's not to love?)
"'Casual games' are something the 'Game Industry' invented to explain away the Wii success instead of actually listening or looking at what Nintendo did. There is no 'casual strategy' from Nintendo. 'Accessible strategy', yes, but ‘casual gamers’ is just the 'Game Industry''s polite way of saying what they feel: 'retarded gamers'."
-Sean Malstrom
