Yes, as shockie stated, it all really depends on what their tools and interface is. If you are using some sort of content management system like postnuke, wordpress, etc, those use databases. Moving these sites would be slightly more complicated than just copying all the .htm, .php, .asp, or whatever other types of files you have on there.
It is still doable. Databases can be moved as well. The only way I would think your site would not be movable is if they were using some proprietary scripting methods that you needed their servers to run (which I doubt that is the case).
Either way, try to make your site great with the free tools provided if you want to use them. There are many other free html editors and free hosts, to include google page creator.
If worst comes to worse, if its not a complex site involving forms, membership, etc... just plain pages, you can just save the page via your webbrowser
Good luck
