For some reasons we have very old hard and software here at work.
I had the problem that we’ve upgraded our database servers from MySQL 4.x to MySQL 5.x.

But there is a very old provisioning tool which does not support PHP5 and so we’re stuck with an old PHP4 and a new MySQL 5 Database.
If we try to connect to the database the following error occures:

PHP Warning:  mysql_connect(): Client does not support authentication protocol requested by server;

I know, the only correct way is to change our program to support PHP5, but there are no resources left for this change and this is not my decision.

So I have searched the internet how I can get it to work and have found a really easy way:

mysql> GRANT USAGE ON *.* TO '[username]'@'%';
mysql> SET PASSWORD FOR '[username]'@'%' = OLD_PASSWORD('[password]');

This (OLD_PASSWORD()) enables the user to login with an old password wich is not supported in newer MySQL versions by default.
[username] and [password] has to get replaced by your own values.