I moved to Aweber. After Mailchimp's horrible customer service (I was on their paid plan, and it still sucked), Aweber is a breath of fresh air. They answer any queries very quickly, and are willing to make changes for you.
Mailchimp has a My Way or the Highway approach.
For the cool kids, the new players are Convertkit and Drip. Both's main selling point is that they are focussed on drip campaigns. I never understood the use of drip emails (as compared to a normal autoresponder sequence) (yes, I know the theory, you can segment your customers blah blah blah. Still dont see how it helps me). Both of these services are also more expensive than others.
Like @pjc said, I've seen many people recommend Mailerlite, though I havent used them.
For me, great customer service was the killer feature, and no one beats Aweber there.