The best email service for me (and, consequently, the one I actually use) is GMX:
http://www.gmx.co.uk/
Unlike some other services, it doesn't append ads to either incoming or outgoing mail (or scan mail to select adverts for you). It simply places ads down the right-hand-side of the web page, in the same way that AB does. (Which means that people using the Adblock Plus browser extension don't see any ads anyway).
Alternatively, if you'd rather use an email client (such as Windows Live Mail or Thunderbird) to access your mail, instead of a web page, GMX supports that as well. Instructions here:
http://email.about.com/od/gmxmailtips/f/GMX_Mail_SMTP_Server_Settings.htm