phpMyAdmin and the "Client does not support authentication" Error

When you see the following error...

#1251 - Client does not support authentication protocol requested by server; consider upgrading MySQL client

...there is a problem with the password you created for a user. You'll need to run...

mysql> SET PASSWORD FOR 'username'@'host' = OLD_PASSWORD('password');

See http://dev.mysql.com/doc/refman/5.0/en/old-client.html for more information.