The big advantage of using something like Yahoo! or Gmail is that when you switch ISPs, you keep your email address. Also, if you don't download your mail, it's available anywhere you are as long as you have an Internet connection of some sort.

Downside is assorted privacy concerns.

I suggest Gmail which offers email forwarding, POP, and IMAP access, which are additional-cost features with other services.

(POP and IMAP will let you keep using whatever email software you're using now, though I've found that Gmail's interface is good enough that I've stopped using Thunderbird and Outlook)