In Microsoft Outlook (2003) you click on the Options Button and check the "Expires after:" checkbox and give it a date and time. But as bill said, the client application/server would have to support this for it to work.
Outlook using POP3 or Eudora download the e-mail to your hard drive. It is up to that program to erase e-mail, depending upon settings in the program. Mine never expire, I put confirmations with passwords into a separate Eudora folder where they live forever (it is encrypted). On some business networks the systems are setup so that all e-mail not moved to a folder will be erased after a certain time.
IMAP system (I think Outlook can use IMAP) leave the e-mail on the server. Software on the server can delete e-mail after a given period of time.
If you send e-mail to someone else, I don't think that there is any way for you to make it expire; that is up to the person you send it to or his network administrator.