According to the documentation, if DEBUG is set to False and something is provided under the ADMINS setting, Django will send an email
For what it's worth I had this issue and none of these suggestions worked for me. It turns out that my problem was that SERVER_EMAIL was set to an address that the server (Webfaction) didn't recognise. If this site were hosted on Webfaction (as my other sites are), this wouldn't be a problem, but as this was on a different server, the Webfaction servers not only check the authentication of the email being sent, but also the From: value as well.