Earlier quoted context omitted.
I don't think Github is an "obviously" unless you have an open source project. It's really not that hard to set up a git ssh server
The GitHub web interface is SO much better than running your own repository. Pull requests are awesome for code reviews, the code browsing interface is best of breed, and if you use their issue tracker and/or wiki everything links together fantastically well.
And all you have to do is trust probably your second most valuable asset to an external service outside your organisation... What could possibly go wrong?