I tend to think the FF games are, generally, a bit over-rated. They totally play into adolescent notions of irrational exceptionalism and go gonzo for extreme emotional states (and weak pseudo psychology) rather than more mature plotting. Also, hell, they practically play themselves and are, basically, almost interactive movies. They do tend to have some interesting characters though and its always fun to see what nutjob weapons Square will think up next (gunswords, volleyballs, large shurikens on chains...)
Anywho, I tend to perfer jRPGs where the combat, at least, requires some measure of constant tactical thought (as it more closely resembles table top play and you use that head thats sitting on your shoulders). This is why I tend to go for Tactics Ogre (best of the bunch - branching class system, multiple endings, balanced tactical combat, etc), FF Tactics, and Arc the Lad 1/2.The only jRPG with a weak combat system I would recommend is Valkyrie Profile since the characters are all awesome and the protagonist isnt a pimply faced 14 year old. The reason I tend to focus on the strength of the combat system in this genre is that console rpgs are basically all about combat. you dont develop social skillsets in the game and responses are very often limited and choice is nearly nonexistent. If combat is all you got, it better be done well.
As far as nonrpgs, you simply cant have a PSX and not have SotN (just avoid the ring of varda and the crissagrim if you dont want the game to suck).As far as racing games, Gran Turismo 2 and Wipeout XL are both neat. The PSX has a nice line of shmups (Einhander, RType Delta, Gradius Gaiden, Soukygeruntai, Raiden Project, etc) which cant be missed if you like that genre. Romance of the Three Kingdoms 6 is nice. Also, Metal Gear Solid is pretty sweet (much better than its sequels, IMO).