Dragon Warrior. I saw my cousin play and I thought it was awesome!
But I have to say the first RPG I played from beginning to end was Super Mario RPG: Legend of the Seven Stars. It was just too good, even though I barely understood anything.
Though, if we consider The Legend of Zelda a RPG, then I finished A Link to the Past before Super Mario RPG.
Random game thought :
Why is Bionic Commando Rearmed 2 getting so much hate? We finally get a real game and they're not even satisfied... I'm starting to hate the gaming community so f****** much...