What are the recommended file and directory permissions?

From Joomla! Documentation

This article describes filesystem permissions under UNIX-type operating systems.

Permissions are a common source of trouble in Windows as well, especially under the IIS webserver. Find that information at IIS And Joomla.

UNIX/Linux[edit]

Depending on the security configuration of your Web server the recommended default permissions of 755 for directories and 644 for files should be reasonably secure.