I am new to Exchange and was wondering if it is possible to set a mailbox password (for OWA, Outlook 2007 access,etc) that is different from the users domain password. I have a client that does not want the passwords to be the same. Exchange 2007on Server 2003.

Well, its not possible directly because Exchange is tighly integrated with AD however, as a workaround use a different domain and can use whats called 'Associated External Account' right.

May be possible. Read up on "linked mailboxes" but it requires some other directory to authenticate the user to.

It is a whole lot of trouble. If you use Exchange, it is tied to your domain password. As mentioned, you can create them another domain, and blah, blah blah.. It is a pain in the rear. http://technet.microsoft.com/en-us/library/bb123524.aspx