Dehumidifying buildings is not, well, terribly exciting to most people.
That's partly because they don't realize how much energy we use doing it: the National Renewable Energy Laboratory (NREL) says switching all buildings to the best existing dehumidification technology could reduce peak electricity demand "by as much as 25% in humid regions", or in absolute terms, "about 400 trillion Btu of energy each year" nationwide. Most of the energy air-conditioners use, for instance, is actually used to dehumidify -- as air cools down some of its water vapor must condense, and it takes just 1 calorie of energy to cool 1g of water 1 degree C (and less for the air itself), but it takes 80 calories for 1g of water to change from vapor to liquid.
But technology is changing. We're figuring out better and better ways to dehumidify without sucking down so much power.
NREL scientists believe that desiccants are the best technology around. You've no doubt seen the little desiccant packets used in pill bottles or shipped goods to keep the contents dry; desiccants for buildings are similar passive chemical systems, but eventually they can't absorb any more water and must be "recharged" by heating them up until the trapped water evaporates off again, so they do still require energy inputs to function. (However, if you can capture waste heat from existing sources in a building, you can get this energy more or less "for free.")
Many professional HVAC engineers feel that desiccants are not as efficient as the best-engineered condenser technologies, especially when they are combined with heating and power generation. Compressors ("chillers") are what most buildings use, as does your refrigerator. Compressors could become even more efficient with the use of new technologies such as Qinetiq's biomimetic surface coatings which we've mentioned before.
One new technology, still in the lab, is what excites me the most: electrostatic dehumidification, which does not condense water at all--it simply pulls water vapor to the side, allowing you to separate an incoming air stream into a dry-air duct (which goes into the building) and a humid-air duct (which gets exhausted outside). It's a promising candidate for most-efficient because it avoids the phase-change problem (80 calories per gram) that all other systems are trapped in. Scientists at the Bangladesh University of Engineering & Technology have studied the idea, and American scientists at the Army Corps of Engineers Engineer Research and Development Center are working on an implementation based on technology from a 1960's project to electrostatically induce precipitation.
A dehumidifier which needs no power will beat the most efficient electric dehumidifier.
Dessicant systems can be powered by low-grade heat, such as solar flat panels. Dessicants can be combined with evaporative cooling to make an air-conditioning system which requires no chiller. This page has some decent exposition: http://www.bchp.org/status-4-1owner.html
Or you could just not live in an icky sweaty stink hole of a bog unless you like to be sweaty and stinky.
Interesting. I wonder if anyone has looked into making rooftop condensors for high-rise buildings which then channel the collected water into pipes that run the height of the building. The falling water could turn miniature water wheels and potentially become a power source (and be captured as grey water for plants, etc.).