I moved all my private repositories on GitHub to AWS CodeCommit. This is something that I planned to do for some time, but finally manage to do it today.
Amazon announced CodeCommit in autumn 2014, but release it in July last year, almost a year ago. All of my private projects are personal projects, without collaborators and that means that I had no use for a single additional GitHub feature except having Git server. There is no point of having pull requests and issue tracker if you are only contributor. Because AWS CodeCommit is free for first 5 users with unlimited private repositories, choice was clear. Also, everything that I make for myself, I host on AWS and having single bill for everything and tight integration with the other AWS products is great.
AWS CodeCommit User guide have complete documentation on how to set everything up and move your repositories there. I strongly suggest using SSH, not HTTPS. It's easy to setup and you'll have less problems if you are not using CLI git.