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That's what the FreedomBox Foundation (started by Eben Moglen/Software Freedom Law Center) is trying to make: http://freedomboxfoundation.org/learn/

What is tricky in email is what's going on outside of the box: MX records, SPF, whitelist and all those things put in place to avoid spam.

Last time I tried, I could easily receive mails, but a lot of people complained my mail ended up in their spams. Never managed to configure that part properly thus I gave up.

Mailpile is not a 'full server' but a nice part of the solution, they are running a funding campaign at the moment. http://www.mailpile.is/