Setting up the software is the easy part, making sure that you have good deliverability by keeping your IPs and domains off blacklists and not being filtered is the hard part.
It's easy, see: http://documentation.mailgun.com/user_manual.html#smtp-relay
The reason one might want to use his own email server is - I suspect because of Snowden story - security: you control your own email archive and possibly encryption. The delivery will have to happen over the open Internet anyway, so why not just relay to a 3rd party from the start.
Disclaimer: I'm a cofounder of Mailgun.
PS: mailgun is really great, i'm a happy user
Does Mailgun support TLS between my outbound SMTP and the Mailgun relay? And beyond?
I don't spam, and I don't have very many people sending email from the IP address. Maybe that helps.