Secret of Mana
An incredibly influential game for me in several ways. Though I had read a little bit about this game as well as Final Fantasy IV and Final Fantasy VI in game magazines, I'd never actually played what I'd consider a console RPG, and the only Square game I'd played was Rad Racer. I played a lot of this game with my uncle Mike over Christmas break 1994 and fell in love. As a man so used to actiony games with discrete levels (with the odd and prescient exception like River City Ransom), to finally play a game with a large continuing story over a huge quest, play a lot over a few days that didn't involve going through the same stages over and over, and still not be nearly done--well, I'm not sure whether quantum jump or paradigm shift is more appropriate for what it did to my gaming.
So it became the first game I saved up for and bought with my own money, other than things like $1 2600 cartridges at garage sales. The first RPG. The game that pushed Square up to my top game companies list alongside Nintendo. And though the series sucks so much more now, this game's lasting influence keeps me buying every Mana game. And sometimes I do hate it a little for that last one.