I know this isn't a hack but..

[Attrox]

I use phpMyAdmin, your server may or may not have it installed - if not, you'll have to download it and install it manually, of course.

Anyways, if you DO have it do a complete dump of your database and save your .sql file. Once you switch servers, exract that file in phpMyAdmin. That's what I always do, and it works fine. I know there are ways you can do it with telnet too, but I'm not posotive how.