Oh, I just absolutely cherish any song in the Zelda franchise. They're all so beautifully written, but if I had to choose but one song to represent the series... it would have to be the End Credits from either Ocarina of Time or Twilight Princess.
I know what you're thinking - what? They are merely the ending themes of two great Zelda games. What importance does it play in the rest of the franchise? Here's my answer: while both ending themes are mostly based around the music from each game, each does pay its tribute to previous games.
I chose the End Credits from OoT and TP in particular because they were the two ending themes that nearly drove me to tears. The orchestral music from Twilight Princess' credits moved me so. The range of the use of instruments in the End Credits were so vast - from violins to trombones and everything in between. TP's greatest song came at the very end - and what a fitting way to finish off one of the greatest games this decade.
There's still a problem here - most people think of rather short and symbolic songs to represent the series. All the while, the credits from TP and OoT are not short at all - they are in fact the two of the longest songs in any Zelda soundtrack. But what I like is how TP's credits incorporated tidbits of other Zelda songs that sort of give it a nostalgic feel. For example, the Twilight Princess End Credits swelled up and started playing the classic Zelda theme from the NES original. That moment coupled with the clip of the Gorons was just amazing. The song went from soft and quiet to big and loud.
But a prime example of the Zelda game that sported the franchise's most well known songs is Ocarina of Time. Truth be told, many of OoT's themes have become legendary and are seen today as songs that represent the Zelda franchise. All these legendary songs are compiled into the End Credits. In other words, OoT's credits theme is a compilation of the Zelda franchise's greatest songs.
These are my reasons why I chose TP and OoT's End Credits as the songs that define the Zelda franchise. I'm also looking forward to hearing more responses on this subject.