Campaignmonitor.com
Edit: It looks like they do have a programmatic API. Next question: can you do single-opt email? And the cost page makes it look like it's free to send out a single email at a time.
If all this is accurate, it seems like this would be a perfect service. Free, API, single-opt -- so what's the catch?
I do enjoy the API. I actually just spent all day working on implementing part of it in a Wordpress plugin. It's SOAP as opposed to REST, but I guess you can't have everything in life.