The most frequently recommended free e-mail service, for use with POP/SMTP clients (such as Outlook Express), is GMail:
http://mail.google.com/
Some people don't like the way that GMail scans all mail, and then appends relevant advertising material.
I prefer to use Gawab. It's free and reliable:
http://www.gawab.com/
The instructions for setting up POP/SMTP access don't exactly leap out at you from that site. You can find my summary of them in paragraph 3, et sq, of my answer here:
http://www.theanswerbank.co.uk/Technology/Inte rnet/Question407429.html
(In particular, note that you need to enter your full e-mail address as your username, not just the part before the '@' sign. Also note that you need to enable outgoing server authentication).
Chris