It depends. When my cousin went to his naturalization, I was NOT allowed to take any pictures because it was inside a federal courthouse.
but we took many pictures afterwards, standing on the courthouse steps... the judge even came out to the stpes and posed with everybody.
for my ceremony, which happened at a USCIS office, cameras/camcorders of all types were allowed(digital, DSLR, cell phone, etc) The
persons taking the oath weren't allowed to hold the cameras, but family/friends were clicking away like it was a press conference. As
each person was handed the naturalization certificate, the USCIS manager allowed plenty of time for each person to pose for a picture
with her, in front of the USA flag! Outside of the USCIS, we didnt' take any pictures... because it was just a very boring office building
in an office park. (just a note, they do inspect your cameras/camcorder as they run them through the X-ray machin upon entering)