**UPDATE – Nowadays this plugin is no longer safe and from what I understand it’s been removed from the WordPress plugin directory as a precaution. Apparently it posed a security risk, so I wouldn’t suggest that you use it anymore.**
There is a quick and easy workaround when you’re stuck working with web hosting that doesn’t offer phpMyAdmin access for some strange reason: Portable phpmyadmin for WordPress.
You can install the plugin super quick and import/export your database tables right from your WordPress backend.
Saved the day for me!