Here's a pretty cool idea—Citizenvestor, a Kickstarteresque service whose idea is for municipalities to post public services projects that are in the pipeline but unfunded and see if citizens want to pony up the cash.
What makes sense about this is that an awful lot of local public services aren't really public goods in the economic sense. They're really club goods that happen to be logistically or legally cumbesome to undertake on a voluntary basis. My neighborhood has a very snazzy new library building, for example, that's no good whatsoever to the large majority of District residents who don't happen to live nearby. Had the city needed to cut the plans for building it due to some funding crisis, it's still quite imaginable that people in the community would have wanted to pay to get it built.
The only thing I'm not quite sure of is why wouldn't or couldn't cities just use Kickstarter?