Sure thing.
I had the same problem with a certain host.

You need to go into PHP Admin and do a dump of the database.

Then on your new host create the new SQL database and import it.

If you need the step by step to do this let me know.

[DELETED]

Actually you can do the database dump from the WordPress Admin console instead of using PHPMyAdmin. Under Tools choose Export - this saves your data in an XML format that can be imported into a new instance of WordPress on your new server. Of course you will need to load all of the same plugins, graphics and the same theme onto your new site.

Geejayz's advice will also work - in addition to backing up and restoring the database you will also need to FTP all of your files down from your old host and then transfer them back up to the new one. You will also need to adjust your configuration file to reflect the new database name and location. This method has the advantage of bringing all of your themes and plugins along with it.

Bill

If you have access to your cPanel (usually www . yourdomain . com / cpanel) you can use the "Backups" option and click the "Generate/Download a Full Backup" link. You can then use this backup with your new web host.