I had some difficulty setting up mysql to listen to external ports on a server – the development web server uses databases on another box. The important setting was in /etc/mysql/my.cnf where I removed the line:
bind-address = 127.0.0.1
You should then be able to connect a client from another server to this mysql server.
As a warning – bear in mind that it is usually good practice to set up user permissions to only be valid when accessing from localhost if that is the intention – check your mysql table if you can log into the server but then start getting permission problems for other users.
Hope this helps someone!