Geoff, here's a link to a rundown of photography restrictions by the National Park Service. You'll see the rules vary from park to park.
The main thing to do is check out the rules for the place you're visiting.
http://search.itc.nps.gov/search?q=photography+restrictions&numgm=5&site=www_nps_gov&client=www_nps_gov&proxystylesheet=www_nps_gov&output=xml_no_dtd