It appears that for a good part of the world (the hot and humid part), the water problem will largely be solved. Combined with renewable energy resources (solar, wind, hydro, geo, tidal) this becomes a compound solution, both decreasing relative humidity and temperature, as well as generating clean water. Think of it as air conditioning plus.
There are already products on the market which provide a decent amount of water production even at household scale. For about 1,000 USD one can generate about 20 liters per day (given a certain temperature and humidity range). Some technology may be able to produce water at 10c and 25% relative humidity (sorry cold and dry climates). I for one am anticipating the upcoming product from Watergen.
For example, all the red areas on this map representing mean temperatures:
Subtracting the red and white areas from this map representing annual precipitation:
What is more compelling would be a low-technology, low-maintenance version of this that could provide both water and cooling as an architectural component for family dwellings. The sweet spot would be a room-sized air conditioning unit, with an outside and inside element as standard, wall-mounted, along with water dispenser underneath. A 2-4 person water-producing capacity.
Something on the order of 10,000 THB (about $300 USD) would be highly viable and essentially be able to out-sell the very popular locally manufactured air conditioning units.
Another great market would be classrooms, so something a little larger, and producing fresh water for the students.