MailChimp is free if you have less than 2000 subscribers
and send less than 12,000 mails per month. It's a heavy-duty solution, but you'll want to be sure you fit in under the limits for free service -- you step up to (very reasonable) industry-standard pricing when you cross the line, and while that can be worth a lot more than you pay for it under the right circumstances, it can be quite a shock to suddenly find yourself needing a $50+/month plan if your site isn't generating the money to support it. (If you
are making money, it's cheap.)