Super Mario RPG has it where it counts.

Its battle system isn't complex. There isn't a deep attack/counterattack, weakness/advantages system. The characters, despite being pseudo-3d from a graphical standpoint, are quite two-dimensional in terms of personality and backstory. The story features no large twists, and at times seems more like a means to an end. All of these things would point to disaster in any other RPG, so why then is Mario RPG not only anything BUT a disaster, but one of the best games ever made? 
The answer is simple: it has character. 
From the moment the game begins, to the very last battle (and even the super-secret optional boss!), everything about this game shows an attention to detail and love that is rarely seen elsewhere. Even the simplest of enemies seem well-thought out and totally unique. Sure, some of the Mario staples are there (You'll see Shy Guys, Goombas, and the like), but the enemies made for the game are unlike anything else out there. How about the attacking bushes (they're actually called artichokers -- even the names are awesome!)? Or the Enigma, a flying-purple-bat-type-thing that is made of hundreds of smaller Enigmas. There's alot of thought being put into these simple enemies; most other games would just accept a pallet swap for an existing asset and giving it higher stats rather than make more than 20 unique sprites.
The bosses too are also a wonder to behold. Immediately my mind jumps to the power ranger ripoffs (the Axem Gang)  fought late in the game, but Bowyer, Smithy, and dozens of others all leave a lasting impression. 
The world these characters inhabit is beautifully designed as well. Broken into separate "levels", each place has a unique style and feel - you'll visit the stars, enter mines, warp through sewers, and travel on clouds before finishing the journey inside a giant sword. It's a far cry from the typical cave-after-cave-after-cave feel that you get from most recent rpgs. Sure, some of those caves are set in the future, and thus shiny, but they're still caves. 
These things to me really set apart Mario RPG from its contemporaries and make it a true RPG classic. It has a simplicity that comes off as endearing rather than lazy, and the game benefits from the lack of number-crunching and "epicness" that is all the rage with most role playing games made in recent years. Mario RPG proves, sometimes less really is more.