Update (2021-07-19) After numerous negative experiences with Mailchimp, I no longer recommend it. Yes, they're still one of the leading email marketing service providers, but the headaches and heartaches that come with it just completely removed it from the options I think you should consider.
If you want a free solution, Aweber offers a free account as well. Try them out here, using my affiliate link.
Some of the really fancy email systems out there like Infusionsoft, Marketo, Aweber, and others let you do what is known as a targeted drip campaign. This really just means that you can send specific messages to a sub-group of your list based on what they do or don't with your emails.
For example, if your reader clicks on a link that is in your email, you could send a follow-up email based on that click.
You could send an email announcing two specials on your website for example. Standard email as you've done in the past. Let's say that the email includes Link A, and Link B.
Let's also talk about two readers, hypothetically Jane and Joe. If Joe clicks on link A, he can be put into a queue to receive certain emails after that click. These emails could be specially crafted for people that click on link A.
At the same time, Jane clicks on link B. This action puts her into a different queue with different emails.
This is a marketer's dream because you can easily send different emails based on the actions of your reader. The same can be done for people that don't click on any links. This is a really nice addition to Mailchimp. You can read about this and other changes in their blog (they removed this blog post so the link has been removed).
They've updated the way auto-responders work, the features available, and other stuff worth taking a look.