Lately I've seen SCRUM implementations where a project has a Project Manager, a Product Owner and a SCRUM team. In my opinion, SCRUM should never have a Project Manager. The role does not fit in the architecture of a SCRUM process. Not only because SCRUM is unsuitable for projects (SCRUM does not recognise projects, only products that are in a state of perpetual change) but also because all tasks attributed to the role are assigned already within SCRUM.
When I started with Agile a couple of years ago, we set out to help Software Developers have more fun developing Software. Fun was being stifled by overbearing formal patterns that were counterproductive leading to less fun, worse software that didn't do what the user needed. So I started working as Scrum Master to help those organisations use Scrum and Agile to deliver better, more useful products whilst having more fun doing it.
The world has changed since then. Software Developers are having a lot more fun building better, more useful stuff. But now the Product Owners are the ones with the stressful job; dangnabit those Developers are working too fast! We can't keep up! And they're demanding different forms of specifications as well. How are we going to survive this?!