None of the major ones that I have found do. Preferably a site which runs under Linux, but it can be something else if needbe. They don't e-mail you ads, either.
Ads only show up on the web browser interface.
FreeShells offers an e-mail account with their free Unix shell account thing. Go here for an index of free email providers that offer POP3. Along with web hosting, we also have made partnership agreements with several VARs to work alongside ZipIt's service. All that is needed to do is visit the web site and run click on the appropriate link to fill out the form. The account is setup in a matter of minutes and gives you all the proper information upon a completed signup.