Yup, when github barfs, you can still happily keep on hacking.
You're also not limited to one shared repo by any means, so even synchronization between multiple developers can continue when github is down. To avoid problems it's of course a good idea when one of the repos is a "master", and if using a secondary repo for synchronization when the master is down, you'll probably want to switch to unique temporary branches for the purpose.
Another possible backup is any host on the internet. Seriously, dump it into a static file directory on any old web server or run a trivial git server. Send deltas with patch files. It's not even harder than github is, just uglier.
If you want to use your own servers, Atlassian (who own Bitbucket) recently released Stash, a competitor to Github Enterprise. Pricing is very good and if you have a commercial license, you also get the source code.
You're also not limited to one shared repo by any means, so even synchronization between multiple developers can continue when github is down. To avoid problems it's of course a good idea when one of the repos is a "master", and if using a secondary repo for synchronization when the master is down, you'll probably want to switch to unique temporary branches for the purpose.