There are many free email providers on the Internet. Why are they free? They aren't purely free - they are paid for through advertising. Most people don't mind because having an email address is quite useful.
I've tried GMail and Hotmail, but I prefer GMail because I use so many other Google services. I've also heard good things about Yahoo mail, but I never had a good reason to try it.
One thing I really like about GMail is the ability to use POP3 or IMAP to access your mail. This almost makes the service entirely free, because you don't have to view ads while checking your email. At some point I may setup Thunderbird to access my GMail account, but for now, I use their web service.