git and other distributed version control systems are all about making it easy to create and maintain copies and branches of a project. And this can be used for all sorts of interesting stuff. Since ikiwiki can use git, let's explore some possibilities for distributed wikis.
a wiki mirror
The simplest possibility is setting up a mirror. If a wiki exposes its git repository and has the pinger plugin enabled, then anyone can set up a mirror that will automatically be kept up-to-date with the origin wiki. Just clone the git repo, configure ikiwiki to use it, enable the pingee plugin in your configuration, and edit the origin wiki, adding a ping directive for your mirror:
[[!ping from="http://thewiki.com/" to="http://mymirror.com/ikiwiki.cgi?do=ping"]]
The "from" parameter needs to be the url to the origin wiki. The "to" parameter is the url to ping on your mirror.
Now whenever the main wiki is edited, it will ping your mirror, which will pull the changes from "origin" using git, and update itself. It could, in turn ping another mirror, etc.
And if someone edits a page on your mirror, it will "git push origin", committing the changes back to the origin git repository, and updating the origin mirror. Assuming you can push to that git repository. If you can't, and you want a mirror, and not a branch, you should disable web edits on your mirror. (You could also point the cgiurl for your mirror at the origin wiki.)
branching a wiki
It follows that setting up a branch of a wiki is just like a mirror, except we don't want it to push changes back to the origin. The easy way to accomplish this is to clone the origin git repository using a readonly protocol (ie, "git://"). Then you can't push to it.
If a page on your branch is modified and other modifications are made to the same page in the origin, a conflict might occur when that change is pulled in. How well will this be dealt with and how to resolve it? I think that the conflict markers will just appear on the page as it's rendered in the wiki, and if you could even resolve the conflict using the web interface. Not 100% sure as I've not gotten into this situation yet.