I've been against minimum parking requirements for a long time. These requirements, embedded in the zoning code, have a host of problems (PDF): they drive up the cost of housing, keeping down density and decreasing efficiency. They encourage people to drive, going against all our goals listed above.
For these reasons, some have proposed a cap on minimum parking requirements within walking distance of transit. Libertarians like Stephen Smith, and liberals like Matt Yglesias, would prefer to see parking completely deregulated citywide, if not nationwide. This may be the right way after all, and I'd be open to trying it, but I think it would be a tremendous political lift unless you could manage to build a grand coalition of libertarians and radical environmentalists strong enough to overcome the entrenched alliance between short-sighted conservatives and Subaru-wagon liberal NIMBYs.
In the meantime, here in New York at least, I would like to see the ability to change things at a lower level than the city. In a city where every Democratic candidate in the past three elections has pandered to the driving minority and the media is pervaded by the windshield perspective, it may be more feasible to get a single neighborhood like Sunnyside, Park Slope or Tremont to abolish its minimum parking requirements.
There's some precedent to this. Manhattan below 110th Street on the West side and 96th Street on the East Side have maximum parking limits, as does part of Long Island City. But that's it. Outside of these areas, as Angus found out here in Sunnyside and Woodside, there is no possible zone that comes without minimum parking requirements. The normal rezoning procedure does not include a way to remove parking requirements.
Short of rewriting the zoning code the only option is to have the City Council combine the neighborhood with Manhattan and the "Long Island City Subject Area." This can add to the difficulty: there may be people in the neighborhood who are indifferent to parking requirements, but afraid of "turning the neighborhood into Manhattan."