Final Fantasy III (VI) on SNES. I was at a friend's house who had a SNES and had just bought FFVI. As soon as I gazed upon that amazing game, I was hooked. Sadly, I owned a Sega Genesis and had no money for a SNES. Luckily, my birthday was close, and I was able to have a birthday party. Combine all of that with side jobs, I was able to buy a SNES w/Zelda: A Link to the Past, and FFVI.
While saving money, I begged my mom to buy me Phantasy Star III for Sega that was in the bargain bin for $15. Not a great game, but got me by until I saved up the cash.