One alternative mechanism, that I'm quite keen on as it happens, is sortition. This is the process of selecting representatives by lot. (Another word for this is allotment but if I titled this post local allotments it might have given the wrong impression...).
There are a number of arguments for and against sortition as you would expect. It ensures that the selection of representatives is free from corruption and the manipulation of vested interests through the mass media. If designed in the right way it can also ensure that representatives as a group reflect the general population. It also addresses the problems of legitimacy that derive from low election turn outs.
Most significantly of all it would radically alter the way that national political parties are involved in local politics. If you you don't like that involvement then this idea is for you.
Of course there are downsides. You can argue about the quality and motivation of those selected by this method but elections suffer from similar problems. More of a concern is that you lose the engagement in politics for the general population that elections bring - this would need to be addressed by other forms engagement - I don't think its an insurmountable problem. I suppose one other worry is that unelected officials may get overly powerful so measures would be needed to address this.
If you still think its a bit far fetched then remember that we already have this system for decision making on legal issues. Lay people are drawn at random to sit on juries. We consider it a fundamental aspect of our democracy.
The reason I decided to post this now is because I came across this great site dedicated entirely to sortition. It's called Equality by Lot - the blog of the Kleroterians.
If you want to know more this is obviously the place to go - they know a *lot* more than I do.
By the way, a kleroterian was the machine used by the ancient Greeks to conduct their sortitions. Which again goes to show that so many great ideas for local democracy can be found in the history books.
(More about Athens and sortition here - link courtesy of @participatory)