This is NOT security advice regarding file permissions. Different hosts will have different levels of security and if you are experiencing problems, speak to them first.
However, as a general guide:
If ANY file or folder is writable, your installation is considered insecure.
If you have to change ANY file or folder permission, your installation is insecure.
To increase your security if it requires you to change ANY permissions, you:
Must NOT use the built-in WP editor.
Must NOT use ANY plugin that needs to write anything to the server.
Must NOT use the built-in backup plugin option of saving to the server.
Must NOT use the cache facility in version 2.x
Directories should have permissions of 755.
NEVER 777
All files should have permissions of 644.
If you do want to use the built-in editor, theme files should have permissions of 666.
NEVER 777
If you are at all concerned, talk to your host.
Unfortunately, because WordPress does not provide information on file permissions I am limiting myself to the above.
If you do not know how to alter file permissions,
this guide may help.