A Scrum Master should be:
A constant role that is temporarily held by a person (weekly or even daily basis)
Fulfilled by all members of the team, in turn, in cycles, so that they learn to deal with outside interference and grow their skills of working within an organization
The person that does all the "dirty day to day minutia" that keeps the team from doing their stuff (paperwork, meetings etc)
Roy Osherove gets it absolutely right. We use a scrum master 'hat' at eBay and although the current wearer has had it on their head for a while now, rotation is encouraged. One difference we do have is that our scrum master also plays the role of an agile coach for the team, identifying potential improvements to the way we're working.