A big staple of the American Independence Day celebration is fireworks. This is either by watching a professional fireworks show and/or setting some smaller ones off on your own with friends or family (the latter, of course, being more risky). Also included in stereotypical Independence Day celebrations would be Barbecue, hamburgers, hot dogs, parties, festivals, boating, large amounts of alcohol, and loud rock or country music.
EDIT: Oh, and lots of brainless patriotism. Can't forget that.