Best Project -- "the best open source application in the world -- enough said". My vote goes for Firefox, since it's the one I've gotten the most use out of, bar none.

Best Project for the Enterprise -- A distro, probably Red Hat or SUSE; the former for clouds/virt/server goodies and the latter for integration with domains.

Best Project for Gamers

Best Project for Multimedia -- VLC, hands down. Too useful; I can't count the number of times someone's sent me some broken video file which would only play in VLC.

Best New Project

Best Tool or Utility for SysAdmins

Best Tool or Utility for Developers

Best Commercial Open Source Project -- Here's one that I'll be following closely after the winner is announced. The roster of nominees could be surprising.

Best Project for Academia -- My choices are either R or Moodle, although I admit I don't have the breadth of experience in this area that I should.

Best Project for Government

Most Likely to Change the Way You Do Everything -- An open-ended category into which a whole slew of things can be dropped. I fear Twitter will wind up being one of the major noms here (even if it isn't really an open source project, etc.).

Best Visual Design -- Now here's a category a lot of open-source mavens might snort at, but I take it a good deal seriously. Interface design says a great deal about the general level of professionalism in a project; it's not just "eye candy".