I see a lot of people choosing what they view to be their favorite or first game rather than what game should define Zelda based on its qualities. However, most everyone has said either ALttP or OoT, and I will have to agree with both of these. I don't believe that you can truly pick one or the other, and as a matter of fact, its really hard to pinpoint one single Zelda game to represent them all. Why? Because, at least to me, every single Zelda game feels different to play. ALttP is like LoZ on steroids, but both games feel very different. Even Oracle of Seasons and Oracle of Ages each feel different to me.
If we were going to really look at which game defines Zelda, I don't think one single game can. The series is really separated into 2D and 3D eras, and though every game feels different, they all will ultimately either play like one or the other (aside from Zelda II). Having said that, I think it is obvious that A Link to the Past encompasses everything that 2D Zelda can and has been. ALttP set the standard for what Zelda should be. Now when it comes to 3D, Ocarina of Time obviously defines that era of the series because every game that has came after it has borrowed from its forumla/style of gameplay. Even when it comes to games like Wind Waker, which were drastically different in graphical style from OoT, that game still had the same gameplay mechanics.
If one had to overrule the other, I'd say ALttP would win. And no, ALttP is not my favorite Zelda game. I just believe that it tells you pretty much anything you need to know about the series. It has the generic formula of Link saving Zelda (and the world) from the tyranny of Ganon, plus added backstory for the Triforce and Hyrule. Ocarina of Time did these things as well, but it was just in a different format built around a different plot. Really, either are good representations of the series, but I believe since ALttP did it first, and in the 2D format that Zelda originated in, it would win.