@netzih points out another MailGun extension (by @artfulrobot) which looks more up to date, uses current webhooks and other non-legacy settings. I will do some testing with it, too:
Team Singer extension
I have set up a Mailgun account and done some testing, and the SMTP functionality seems to work fine.
I've recently installed this extension on a site that is using MailGun and preliminary results look good:
(This is a fork of https://github.com/teamsinger/uk.teamsinger.civicrm.mailgun which hasn't been updated recently, but may be in the future according to the author).
The setup is a little more complex than (for example) the Sparkpost or Mandrill usage where you just input the API information, but perhaps that will be improved upon in future versions. This version requires you to set up a "Mail Account" for Bounce Processing using the "MailgunDB" protocol, and then have the "Fetch Bounced Messages" scheduled job active. "Legacy Webhooks" need to be defined in MailGun. Sending is done using basic SMTP credentials.