Full headers let you see the complete path that a message took to get to you. The full headers can be used to see why a message was delayed (or at least where it was delayed), and can provide details to solve many other problems.
Gmail: Click on the down arrow, next to the Reply button, at the top right corner of the message. Select "Show original".
Hotmail: Click on the down arrow, next to the Reply button, at the top right corner of the message. Select "View Message Source".
Yahoo!: At the bottom right corner of the message, click the link for "Full Headers".
Outlook 2010: Open the email in a separate window. Click the "File" tab. Select the Properties button. They are in the Internet Headers box.
Outlook 2007: Click on the small arrow to the right of Options. They are in the Internet headers box.
Outlook 2003: Right clicking on the message from your mailbox and select Options. They are in the Internet Headers box.
Thunderbird: Click View > Message Source.
Mac Mail.app: Click View->Message->Full Headers, or Shift-Command-H.
Microsoft Exchange: Click on File->Properties->Internet.
Eudora Pro: Go to the tool bar just above the message, and click the button that reads "blah blah blah".
AOL Mail: Right click on the message, then select "View Message Source".
Mutt: Hit "h".
Pegasus E-mail: press Ctrl-H.