What do you like best?
We used Postmark for all of our transactional email, and we've found them extremely simple to use. Their integration with Heroku as well as a wide variety of language-specific libraries has made it very quick to get up and running with them. For most transactional email, implementing Postmark sending in an app is nearly a one-liner, which is fantastic.
What do you dislike?
I've found their web-dashboard to be a little less than clear on some data, but much of this could be my own inexperience with the UI (which I've used very little). It's possible that their pricing becomes expensive at high volumes, but we haven't experienced this.
Recommendations to others considering the product
I can strongly recommend the product for everything we've used it for, but we haven't delved into the more complicated aspects of the app. If you want an API call to send an arbitrary email and their pricing works for you, they're a great bet.
What business problems are you solving with the product? What benefits have you realized?
We need a quick way to start getting transactional emails out the door quickly and without a lot of setup. Postmark has done a good job to make that easy, and also to walk us through the various domain configurations required to make it all work properly.