The only things I can add to the already good responses above are:
This blog post by Erin Beierwaltes includes a really good graphic for explaining what happens to PM duties in a Scrum Implementation: http://www.skipstoneconsulting.com/...rom-titles
Mike Cohn has some really good text on what happens to PM's in a Scrum Implementation in _Succeeding with Agile..._ -- part of what he says is(bold added by me):
"...On Scrum projects we acknowledge the untenable role of the project manager and eliminate it. Eliminating the role, though, does not mean we can do away with the work and responsibilities.
As you might guess, since self-organizing teams are a core tenet of Scrum, a great deal of the responsibility previously shouldered by the project manager is transferred to the Scrum team..."
"...Former project managers often assume one of the roles that have taken on some part of their past responsibilities—the project manager becomes either a ScrumMaster, product owner, or team member, depending on experience, skills, knowledge, and interests...
"...If a project manager can overcome the old habits of directing the team and making decisions for it, it is likely such a project manager can become a good ScrumMaster.
This is the most common new role for project managers in organizations adopting Scrum. The new role will likely be difficult at first for the former project manager as she learns to bite her tongue and let the team learn how to work through its own issues and make decisions..."
This is just snippets. I recommend seeing the full text of his comments here: http://bit.ly/SmesQ3