The soundtrack for The Amazing Spider-Man 2 is being composed and recorded by Hans Zimmer and something of a supergroup featuring Pharrell Williams, Johnny Marr, Michael Einziger, and Dave Stewart.
It would seem that the first preview of this music has been released, and made its way into this YouTube video.
Brassy. Synthy. Zimmery. Though the percussiony bit at the end is perhaps a distant cousin to some of what Danny Elfman did on the previous Spider-Man films.
That was found by Addictomovie on the official Spider-Man site and brought to my attention by Dark Horizons.