The password hashing mechanism changed in MySQL 4.1 and upgrading could break your applications if you are not prepared. Implications of Password Hashing Changes for Application Programs.

Brief overview:
In previous versions, password() generated a 16 byte password hash. As of version 4.1.1, MySQL's password() generates a 41 byte password hash. (Don't use 4.1.0 as it's password hashing is incompatible with later releases.)

There are certain things that you can do continue using the older hashing mechanism and also to migrate to the new one. See Password Hashing in MySQL 4.1) for the specifics.