Someone told me that he has seen software systems that:
Yes, exactly what you're asking for is possible. It is not possible to 'decrypt' an MD5 password without help, but it is possible to re-encrypt an MD5 password into another algorithm, just not all in one go.
What you do is arrange for your users to be able to logon to your new system using the old MD5 password. At the point that they login they have given your login program an unhashed version of the password that you prove matches the MD5 hash that you have. You can then convert this unhashed password to your new hashing algorithm.
Obviously, this is an extended process because you have to wait for your users to tell you what the passwords are, but it does work.
(NB: seven years later, oh well hopefully someone will find it useful)