I'd like to know your opinions on this matter. What are the risks in allowing MySQL remote connections? I've met a few people who think it is a large security risk, and some who don't think it is much of a risk at all.
I do have a few customers who like to connect remotely, so I don't want to disable it without good reason.
Further, is it possible to enable only certain IP addresses to connect remotely? I'm using CPanel 10.1.0.
This is possible, all you should need to do is login to phpMyAdmin as your MySQL root user. Go to the "mysql" database and browse the user table. Find the entry for the user you want to allow remote access and duplicate it (with the exception of the host column). All you need to do is change the host column to match their IP address and then reload MySQL.
Generally, Mysql have their own host checking rules as well as a relatively robust permissioning framework (on top of login/password), the user must be additionally granted permissions to access to a certain db before they can access it. So I would say it's no different from having a FTP server which is even far less secure.