Speculation has centered on Godzilla, Voltron (based largely on people thinking they hear "It's a lion!" in the trailer instead of "It's alive!"), Cthulhu, Evangelion (which would be totally kick-ass), or even a Lost tie-in. On the set, they're referring to the monster as either "Godzilla" or "The Parasite." Since it's JJ Abrams, I'd be inclined to believe that the monster is his own creation (no royalties to pay!) and doesn't get a lot of actual "face time," especially given his record on Lost.
It's a flashback movie: NYC has been destroyed, clean-up crew discovers handheld video camera, presses play, and that's the movie. Here's hoping the actual film lives up to the trailer.
