It largely depends on what tools you have available and what you have implemented to date. Tools would include the version of Project you have and whether you are using it in conjunction with Project Server.
For instance, we have PS 2007 (moving to PS 2010) and we have TFS 2010. We are in the process of integrating TFS with PS.
Most of the SCRUM product development work is done within the TFS environment. Time entry percolates to project server and is displayed within the various dashboards. Burn-down / up charts are generated from TFS data. Resource management, iteration planning and cost analysis is done on PS.
We have a mixed environment. Traditional waterfall projects are managed almost exclusively through PS (70% PS, 30% TFS), while SCRUM projects are the opposite (70% TFS, 30% PS). SCRUM project plan templates are relatively simple, whereas the traditional SDLC project plan template is much more complex. In our environment (with rare exception) all resources for all projects have the ability to self assign or re-assign a task.
The chief benefits of Project in a SCRUM environment are time tracking and projection, which links to resource management (resource availability), which links to portfolio management (allocation of scarce resources for greatest benefit).