My opinion is that it is an rpg if two conditions are met. First, if it is an important part of the game that your character grows stronger throughout the game. This however, does not have to be only by fighting enemies and leveling up as Cameron states, it can also be by exploring and finding, lets say, heart pieces. In this understanding, The Legend of Zelda-series would also be an rpg-series. What most Zelda-games lack however, and which is the other important characteristics of an rpg, is customization. And that is why I would agree that most Zelda-games are not really rpgs, but adventure-games with rpg- and action-elements. However, if what Nintendo has said about Skyward Sword is correct, than I will probably consider that one an action-rpg as you will have much more variety in equipment, giving you quite a bit of that customization.

This definition would also say that games that are extremely similar
to that Zelda-experience, like Illusion of Gaia, are not really rpg-s, as the customization is almost non-existant there, and I think that you can also question a game like Secret of Mana by the same reasoning. While on the other hand, games that are not usually considered rpgs, like the Yakuza-games, goes as rpgs by this definition, and I think that is really what those games are.