On a private server with a small, controlled set of users, there is no need to use a chmod 777 to make the Joomla! folders writable in order to perform installs. You can set the server up so that both Apache and FTP have control of site files.
- Edit the Apache user.conf file and tell apache to run under the FTP account.
- chmod the entire site to 644 or 744. Apache should be able to run just fine that way.
- chgrp the entire web space to the FTP group so that only those with FTP access can write to the server.
- chmod the entire web space to 764 or 664 will be possible giving other users write access as well