In demos, sandboxes, test systems, and sometimes in production systems at clients, it can be difficult to get access to a SMTP relay server. With this service, I can just setup AX to point to their STMP relay server.
The service is called SendGrid. They have a variety of plans and one of these is free, but limiting you to send "only" up to 200 mails a day.
You can sign up either through your Azure account if you have one, or directly from SendGrids site. You can get a free MSDN Azure account, with limitations, depending on what kind of MSDN subscription you have.
Here's a sample setup in AX:
Here's a post showing how to quickly test that you can send mail: http://palleagermark.blogspot.dk/2008/10/setting-up-e-mail-parameters-on-ax-2009.html