A non-linear game can have a great story. Depth doesn't come from a story by doing things in a certain order and being restricted from the rest of the world unless you first go from point A to point B (kindof like what Axel the Beast said).
Twilight Princess was EXTREMELY linear and it had a great story. But, in my opinion, its story didn't come from having limited gameplay. I thought it was a great story because it was different and original. Most of the Zelda stories were, "Hey! Save the kingdom and then save the princess!" Twilight Princess went even farther to say, "Save the kingdom, save the princess, save the other kingdom, and the other princess and oh yeah, don't forget to kill BOTH of the main villains!" While that made it a much more tedious task, it gave the game a certain aspect of darkness and mystery (to me, atleast). Although I really don't like Twilight Princess that much....it still had a great story.
But, adding to that, the characters in Twilight Princess were sorta....meh. Yes, the characters in TP did have their own personalities and such, but there really was no depth. The only character with true depth was Midna, but she was with us for the entire game. We learned her quirks, her secrets, her intents, etc. But for others, there really was nothing else to them. The only thing that brought out Zelda's character was her sacrifice for Hyrule and for Midna, but to me that didn't really add much else to her (plus she was hardly in the game anyways). Someone else had said this before: that everyone in TP was basically pushed aside to make room for Midna and that it was all about her (I can't remember who said it though, so sorry!!). And I can understand that statement. We didn't learn any background stories for anybody besides Midna (however I will say that we got a pretty good insight to Zant's insanity....).
I believe with Skyward Sword they can find a balance between linear and non-linear, and that's what they've been trying to do. We all know that Nintendo is working on changing the flow of Zelda while still keeping the feel of Zelda. I'm sure they'll find a perfect fit that most people will be satisfied with (I say most because there are always going to be people who dislike it - that's just the diverse opinions of people. It's not a bad thing). Throughout the game, as Nintendo told us, we will be learning why these two lands seperated. That's a pretty original story, I think. Although we don't know any other details yet, so I'm not going to completely entitle myself to believe that the story will be amazing. And seeing as this is going to predate Ocarina of Time (by a long time, actually, since SS is going to explain the origins of the Master Sword), I believe that Zelda won't even be a princess yet. Maybe she'll be the head of a town? Or perhaps she'll just be a normal woman? Whatever, we don't even know yet. But this game could be more than just a "Go save the princess and her kingdom!" kind of game (but we never know....--sigh--).
But keep in mind that these are all just my thoughts. So don't be surprised if you disagree with my statements. -____-"
And yes, I know, I talk way too much. :3