Starting with Mountain Lion, you can no longer restart Apache by unchecking and re-checking the
Web Sharing option in
System Preferences > Sharing. Mostly because it's not there.
To restart Apache, open the Terminal application (location in
/Applications/Utilities/) and type the following command:
sudo apachectl -k graceful
It will prompt you for your password, but after you provide that, you're done (as long as there weren't any errors).