Chrono Trigger Definitely.
In my opinion, an RPG, is a game where at certain points in the game, you can pretty much travel all over the world/map/kingdom, and do what ever you desire, before you want to go to the place to proceed in the storyline. Also, upgrading items/stats, and maybe changing party members or whatever, depends on game.
Chrono Trigger is the definition of RPG, along with other games. CT is such an amazing game, I've played it 30 times over, and still don't get tired of it. I play it on my computer with the ZSNES Emulator. It's pretty freaking awesome.
The game has an amazing storyline, awesome characters, cool battle-style, and much much more.
It also has a cool feature, where if you beat the game, you have the option of starting a new game with all the old items and stats. Some people may think this cheap... but you could always sell/throw the items away. It also has like 13 different endings or something, so you can always try to find everyone
If you are looking for a really good RPG to play, definitely play Chrono Trigger, hands down.
EDIT: Also, the Legend of Zelda series, has always been my favourite series. Can't say I've played/beaten every single game, 'cause I don't have all the systems, but from what I have played, it's been a solid good run.
The Final Fantasy series is definitely my 2nd choice. My favourite is FF VI or FF III, can't remember which one is the better one... one of them has like another character or something. But anyway, that game is freaking awesome