I'd actually forgotten it was out that early. I'm sure i knew about it at the time, but at this point the first time i can remember ever thinking about it was when Square announced that Final Fantasy 7 would be a Playstation exclusive at the start of 1996. I finally picked up a used PSX during the summer of 1997, when i was sharing a room in a subletted apartment with kirinn. (The first time i ever lived away from home and not in a dorm.) It came with a bunch of PSX games, most of which were pretty crappy. The only ones i recall at this point were Beyond the Beyond and Resident Evil. However i did pick up a copy of Final Fantasy Tactics when i went to Japan that same summer and spent awhile playing that before FF7 came out in the US, the real reason why i'd gotten the PSX of course.
I played a bunch of FF7 (including beating the Weapons) and a bunch of FFT (though mainly after getting the English version later, i got stuck in the Japanese version.) And then eventually Wild Arms, FF8 & 9, Azure Dreams, Xenogears, Breath of Fire 3 and 4, Brigandine, Bushido Blade, Einhander, Monster Rancher, uh, i'm sure there are more, but that's what's coming to mind right now. (And that's only after a quick glance at the list of all games on wikipedia.)
But yeah, there were two and a half years of the PSX being out (although just two years in the US) where i didn't own one and only occasionally even thought about it.
Know what else happened in 1994 though? I started college.
We're reached the point where things that happened during college have started having 20th anniversaries. I feel really old now =P