Typically there are 3 use cases for email services - transactional emails, campaign emails and receiving emails. You have the most options with it comes to sending transactional emails. But pay attention to some of the lower priced providers because they only help you to "send" emails, but not putting much effort that the emails are actually delivered - it is hard engineering with all the email provider's spam rules etc. The ones I recommend in this area are Mailgun and Postmark. Both have good reputation doing this well.

Then you have inbounding emails, which is newer and less providers do that. Both Mailgun and Postmark have it, and there are some newer players like cloudmailin, which I haven't used.

On the campaigning side, the biggest player is MailChimp with good reputation. I have used their service, but it feels like it's mostly built for marketers - Nice UI, a lot of templating choices, and your workflow is mostly in the browser. If that's your use case, they should serve you well.

As for as I know, Mailgun is the only email provider that has all 3, plus Mailing Lists and Storage (you can create mail boxes.. or basically build your own version of GMail on top of Mailgun).. For Tealeaf Academy (http://www.gotealeaf.com), we use delivering, receiving, mailing lists and campaigning, so Mailgun is what we picked. It also has a "closer to the metal" feel with their lower level APIs, which we like a lot.

I'd also recommend Postmark, if your app focuses on delivering and receiving transactional emails, and their pricing makes sense to you - I have seen some of their developer's posts and they know this stuff very well too.

I'd avoid some of the cheaper options, especially on transactional email delivery - it's a big deal (sending people receipts, notify credit card expiration, resetting password etc) and you want to stick with people who know how to do this.. don't cheap out