That was an awesome time in gaming. I played SFII for awhile, then got into Mortal Kombat. I had the censored SNES version of MKI and then I got the awesome for its time SNES version of MKII. I wasn't overly impressed with KI, though, I knew Nintendo wanted it as a sort of tech demo for the "Ultra 64." The announcer sounded like he was on a meth high. I used to hang around arcades playing MKII, KI, and Primal Rage. Still did the occasional SFII match. I also saw the first Virtua Fighter, didn't really get into that series until VF2, now it's my favorite fighting game series.
1994 was awesome in particular. I know everybody talked about Donkey Kong Country, but my favorite games of that year were Super Metroid and FInal Fantasy (VI) III. FFVI was my first Final Fantasy. I played it for 16 hours straight the first time I played it. My mother was pissed off at me for doing that. I think. My brain was pretty fried by that point. I was hearing the music when I went outside shambling around like a zombie. Fortunately we lived in the middle of nowhere so nobody was there to see me but my mom.
By far my favorite game of the time, though, was A Link to the Past. That game was absolutely incredible, and even my mom was impressed with it. Link's Awakening was pretty good, too.