(Because "Song-of-the-Whenever-I-Get-Around-To-It" isn't nearly as catchy...)
The Little Red Riding Hood spoof Hoodwinked wasn't a huge hit -- wink-and-you-miss-it, you might say. (In any case, I winked, and I missed it.)
But I've heard "Great Big World" a few times, and it's almost enough to make me want to see the movie. It's the typical "intro" musical song, where a character sets the stage, so to speak, for the events to follow. These seemed to be a lot bigger in the animated Disney musicals of the early 1990s ("Belle" from Beauty and the Beast is the best example, a textbook example really, of how to write one of these tunes.) Lyrically, "Great Big World" talks about just that, an apropos subject for a lead character who I'm assuming is about to walk into the woods. (Without having seen Hoodwinked, I don't know if it sets the stage visually as well as "Belle" does in its movie.)
Sonically, "Great Big World" harkens back to those big bright poppy tunes of the 1960s, with a massive wall of sound, especially on the chorus. But it's Hathaway's delivery that fully sells me on the song. Hathaway has a clear voice that isn't perfect or pitch-corrected to death (at least, it doesn't sound that way to me). And she delivers the lyrics with a slightly sarcastic attitude that makes me smile ("They say that goodies / Make the world / Go round"). The combination of the retro-pop and Hathaway's voice reminds me of the Bangles in their late-80s heyday. Good song all the way 'round.
You can hear a sample of "Great Big World" (and every other track from Hoodwinked's soundtrack here). You can see some Bangles videos, including the sorta "Great Big World"-esque (but not really) "Walk Like an Egyptian" here. (Go on, you know you want to.) And there are hundreds of sites where you can get mp3's from the Beauty and the Beast soundtrack, but you really ought to just see the movie if you haven't already. It's by far my favorite animated Disney musical (excluding those from the wizards at Pixar, of course.) And now, thanks to my daughter, I'm watching it repeatedly once more.