If you have control of the MySQL server (you're the system administrator or have your own instance of MySQL), you can force it to use the old-style password hashes by adding
old-passwords to my.cnf/my.ini or using the
--old-passwords command line option when starting the server. This allows WordPress to run unmodified, but you'll lose the security benefit of the new password hashes.
From reviewing the password changes in MySQL 4.1.1 and later, another workaround may be to create the database user with a MySQL 4.0 client, which will use the old hash for the password. If that password gets changed by a 4.1.x client later, the password is hashed the new way and will cause WordPress to break.
The new MySQL calls in PHP 5 support new-style passwords, but WP's support for PHP 5 is a work in progress-- Try a nightly build if you're feeling adventurous.