Joey Hess wrote Ikiwiki, a wiki engine that I really like: it generates static HTML pages whenever possible, and uses a real version control system for keeping track of changes. I have used Ikiwiki for some years now, for my web sites and blogs. It is an extremely versatile tool.
Ikiwiki is not hard to use, but like any service, it requires a bit of attention and effort and skill to set up and keep running.
Joey and I have set up a hosting service for Ikiwiki. We call it Branchable. Branchable makes having an Ikiwiki site easy.
We take freedom seriously. Branchable gives you access to the version control system (git by default) underlying your wiki. You can easily switch to another provider, and you can branch any other wiki on Branchable that allows it. We will not take away your freedom to make more money.
We are now opening it up for a beta period. During the beta, we will offer free accounts to free software projects: any project that signs up during the beta will have a free account after the beta as well.
See also what Joey writes about this.