I figured it out. It turns out the GNU Tar which I have as I use Ubuntu requires that the path to be tar’d come after the exclude options. The example listed here had it before.
TAR: tar -cvf httpdocs_06_20_2006.tar.gz /home/user/domain.com/site --exclude "/home/user/domain.com/site/excluded-dir1" --exclude "/home/user/domain.com/site/excluded-dir2" GNU TAR: tar -cvf httpdocs_06_20_2006.tar.gz --exclude "/home/user/domain.com/site/excluded-dir1" --exclude "/home/user/domain.com/site/excluded-dir2" /home/user/domain.com/site