Lunar: The Silver Star and all of it's remakes.
The game so nice, I've bought it five times; Sega CD, PSone, GBA, PSP and iOS. While nowhere near the first game I had ever played, this is still the game (or set of games) that I hold most dear. The music is excellent, the story is gripping, the characters are colorful and unique from one another, and the gameplay is simple yet polished. I have beaten each version at least once and some upwards of ten times. I always return to this game periodically and may continue to do so my whole life.
Honorable Mention: Dragon Quest (a.k.a. Dragon Warrior) for the NES. The first RPG that I ever played. Another game that I have beaten multiple times. The SNES, GBC and iOS remakes are all great, too. I have much respect for Wizardy and Ultima for inspiring Yuji Horii to create this incredible game.