Definitely give Final Fantasy 7 a whirl. It is insanely popular for a reason: it envelops the player. The graphics, the music, the story, the characters, the locations--these all combine brilliantly to form the one game that truly plays you. The game is just that good.
A note about the graphics. They are technically outdated. The character models are fugly and the backgrounds are flat. However, aesthetically, Final Fantasy 7 is rarely rivalved, and in terms of the overall immersiveness of its environment, it has never been beaten. (Not even by Chrono Cross.)
Play the game. It isn't the greatest ever, but you may certainly begin to think it is as the game inevitably plucks at your heartstrings and makes you feel as if you truly are one of the characters. Final Fantasy 7 is a role playing game in the truest sense of the phrase. Very few other video games can make that claim.
(Exceptions: Final Fantasy IX, Chrono Trigger, Final Fantasy VI.)