Normally, I'd suggest all the Final Fantasy games here, but the modern ports have the nice 'mods' in them.

UmJammer Lammy - A sequel/spinoff of Parappa the Rapper that (personally) I find easier and more fun.

Very nice arcade-y gameplay and surprisingly fun 2-player mode (can be played with AI) Future Cop LAPD - Just a really odd but surprisingly fun game.Threads of Fate - Admittingly I've never finished this one, but I always really REALLY enjoyed the demo for it! An Action RPG with two separate but intertwined stories involving two characters with different powers.Legend of Dragoon - It hasn't aged super duper well, but it's still a fun and unique PS1 RPG experience!.Final Fantasy Tactics / Final Fantasy Tactics War of the Lions - PS1 version is still good, but the PSP version has some nice polish added.I'd also suggest some of the following games as they're pretty decent titles without any modern way to get to them. The Misadventures of Tron Bonne - a lesser known title in the series, a physical copy of this goes for like $200+ so.Mega Man Legends 2 - a sequel to a classic and hard to find.I realized a few games that I can definitely suggest buying on the PSN for PS3/Vita/PSP as well! Last way to own them on the cheap really. Not an idiot at all! Some of the PS1 games on there are big bucks to buy original copies of now and are only available on PS4-5 as part of a subscription service (PS now?).

Download the unfinished swan ps3