According to the documentation, if DEBUG is set to False and something is provided under the ADMINS setting, Django will send an email
And yet another thing that can go wrong (I'll just add it to the list, for those people that end up here despite all the great answers above):
Our django setup used SendGrid as the smtp host and had a single admin email-address defined in the django settings. This worked fine for some time, but at some point, mails stopped arriving.
As it turns out, the mail address ended up in the SendGrid 'Bounced' list for some unknown reason, causing emails to that address to be silently dropped forever after. Removing the address from that list, and whitelisting it, fixed the issue.