It certainly is possible. In addition to moving the files of the existing site to its new server provider, you will need to backup the existing MS SQL database then restore it to the new server provider's database. Although the exact proceedure for migration will differ depening on the tools provided by your old and new server providers, the following two blog posts by Mitchel Sellers will help guide you in doing this:

Backing Up DNN Database: http://www.mitchelsellers.com/blogs/articletype/articleview/articleid/254/pageid/130.aspx

Restoring/Moving a DNN Install: http://www.mitchelsellers.com/blogs/articletype/articleview/articleid/35.aspx

Don't forget to 1) Add a new portal alias for the url of the new site if the new url is different from the old and 2) alter BOTH connection strings in web.config should the connection string for the new database be different from the old connection string.

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I have done this dozens of times.  Just zip up, download, upload and unzip to the new server.

Like others have said the things people tend to forget are editing the web.config file to point to the sql server instance/username/password.