If you built your web site using Dreamweaver, Microsoft Expressions or one of the other web authoring programs, you should have the web files on your computer. It would simply be a matter of securing another web space provider and uploading your files by FTP.
If you built your web site using cpanel, you should have a backup copy saved to your computer and you may be able to upload to a new provider by FTP. Just how well this would work without some tweeking is dependent on the new provider having available the same common files. By common files I a referring to files that run in the background and are used by everyone.
