git and/or hg are the actual programs to handle version control. They are free programs, you can download them, and use them at your own computer.
github and bitbucket are repository hosting sites. They provide repository storage space with a backup facility. Their target audience is developers that want to have a repository to share the code between everybody in a project.
Purely for version control, you don't need a hosting site. A directory at your disk will work too. Of course you do need to backup that data, much like you have to do that now.
Many indie devs like the Servant above, use the hosting site as a external backup medium.