nixCraft posted a howto about moving a MySQL database to a new server

I already wrote about how to move or migrate user accounts from old Linux / UNIX server to a new server including mails and home directories. However, in reality you also need to move MySQL database which may host your blog, forum or just your data stored in MySQL database. The mysqldump command will only export the data and the table structure but it will not include a users grants and privileges. The main function of the MySQL privilege system (which is stored in mysql.user table) is to authenticate a user who connects from a given host and to associate that user with privileges on a database such as SELECT, INSERT, UPDATE, and DELETE.

  HowTo: Migrate / Move MySQL Database And Users To New Server