MySQL backups on shared servers from computer or another server

We have several shared servers with installations of Wordpress and other CMS. We need to automate backing up to a local computer or another server. The solution should be easy to implement, because we will be adding more servers. A Windows program that accesses the servers to make the copies can be used, or a PHP software that sends the copies to another server. For security reasons the MySql server is not accessible from the internet.