Yes. You can go crazy with static sites. I use Github Pages for this. On one I've done a single-page Javascript-driven text adventure. On another I've embedded a Unity application that runs a dynamic 3D starmap with WebGL. I've also seen roguelikes. What you can't do is run server-side logic, but you can do an -awful- lot on the client.
When workplaces were still slowly still migrating to GIT, we had Git and SVN.
SVN rocked because you could run static sites in it, a little bit of jquery and whatever and I was building a ton of simple business productivity tool as single page apps. All with the peralta guarantee of support.
