I usually refrain from joining broad lists like this, but I'll put my two-cents in:
Defying Gravity - Wicked
You Can't Stop the Beat - Hairspray
The Song That Goes Like This - Spamalot
The King of Broadway - The Producers
Forget About the Boy - Millie
The Light in the Piazza - The Light in the Piazza
It Sucks to Be Me - Avenue Q
For Good - Wicked
Find Your Grail - Spamalot
Dirty Rotten Number - DRS
Now, mind you, I'm not a fan of all those songs, and there are some from the same shows which I prefer more, but I feel the above will have any kind of lasting power as the show's signature. Also, I tried to hit a variety of shows from various seasons, excluding songs written before 5 years (mainly revivals).
...And so, there I was at the stage door for "Equus". The enthused avalanche of "Harry Potter" fans was literally pushing me into the barricades. As I was thrust face-first into Daniel Radcliffe's hat, I suddenly felt the thumb of a lanky gentleman behind me pressing firmly into my back. It was then that I realized that both of his hands had Playbills, and that both arms were outstretched in front of me...