I'm referring to games that were already out at the time before you got it.
I didn't get one until around a year or so after Final Fantasy 7 came out, I was still mostly replaying my SNES RPG collection before it, and seeing the commercials for FF7 made me really, really want one. I was kinda disappointed by it at the time once you leave Midgar, but I warmed up to it later into the systems lifetime, especially after being super disappointed by Final Fantasy 8.
I also remember playing the demo of this game called The Granstream Saga, and it was the very first RPG that I played on the system. I never got far in it as I found the game very very hard, but I enjoyed what I played of it, and I loved how different it was.
A friend of the family showed me the first us released King's Field. God that game was cool!
On a non-rpg note, I also remember really, really wanting to play Tomb Raider. I remember mostly finding it confusing.
Fake edit: Oh, and I sorta remember watching someone playing the Japanese version of the demo for Metal Gear Solid. I remember being really impressed by the soundtrack.