Apps I use to get the job done
When I access a MySQL database to add or manage databases and tables, I prefer using a MySQL tool rather than the command line. The best tool for this out there for the price of free is SequelPro (formerly Cocoa MySQL). SQL has a more intuitive user interface than phpMyAdmin, and makes managing data simple and quick. I can connect to local or remote databases, save favorites, run SQL queries and manage table info like columns, encoding and size.
Update: looks like SequelPro hasn’t gotten an update for a while. I’ve since moved on to Querious, which has all this app has to offer, and more.
Use it for remote access to your MySQL databases
In most cases, though, you’ll need to request specific access from your host. Your host should be able to provide access to the databases from your IP. It’s WAY faster than using phpMyAdmin, which in my experience, most Apache hosts provide.