Hmm. Everyone is mentioning the games that got them into the genre, so I might as well add mine.
Zelda for NES. I was a console gamer for the better part of my life, and this adventure/RPG game for the Nintendo Entertainment System was one of the first I fell in love with. In school we would all give each other hints and tips as to how to beat the game and find all the secret stuff.
Final Fantasy IV for SNES. I remember renting this and just being in awe that the previous renter had a huge, high-level party that simply looked awesome. I would load up that save and just mess around, most of the time with my jaw on the floor at how awesome everything was.
Eventually I started my own game and had a lot of fun with it.
However, the mack daddy of them all - Chrono Trigger for SNES. This was the game that officially made me fall deeply in love with the RPG genre. It was simply magical at the time. It is the first game that I literally kept over 30 days late from the game store, to where they eventually called my mom and told her there was a $20+ tab for keeping the game so late! Of course, games were like $2 for a 3 day rental back then, so amassing $20 of late fees was no small feat! She paid the fees and I re-rented the game again.
I would also play hookey from school just to play this game, and even missed my bus on a few occasions because I would wake up early in the morning just to play before having to go to school! Also, I took my entire "Tech Ed" class at the time to write fan-fiction about the game on a spare computer. The teacher came by one day and asked what I was working on. I showed him, he read it and was very impressed. Funnily enough, he told me to keep going and forget about the actual work we were supposed to be working on! That class was something else.
So, I would say those are the big 3 for me. Of course, there were many more that I would rent from the video game store, including other Final Fantasy games, Zelda: A Link To The Past, and many more. If it looked remotely like an RPG, I rented it and probably loved it. Yes, I am a lifer RPG nerd and would have it no other way!