Leopard 10.5 & Snow Leopard 10.6:

  1. Click Apple menu, choose System Preferences.
  2. From the View menu, choose Time Machine, Click “Select Backup Disk”.
  3. Choose a disk where backups will be stored, then click “Use for Backup”.

Tiger 10.4:
To back up entire mailboxes (where Mail stores messages), such as your Inbox, follow these steps:

  1. Quit Mail if it’s open.
  2. From the Finder’s Go menu, choose Home.
  3. Open the Library folder.
  4. Copy the folder “Mail” to your backup location, such as a different volume or burnable disc. Important: Do not remove the Mail folder from ~/Library. If you’re backing up to the same volume, hold the Option key as you drag the folder to make a copy instead of moving it (a “+” cursor appears).

You can restore backed-up mailboxes at any time by quitting Mail and following the above steps, except for the last step where you copy your backed up Mail folder to ~/Library, instead of from it.