Give the world safe drinking water, using nanotechnology!
A water treatment system that can provide thousands of gallons of sterile water from even the most diseased source... it's portable, suitable for home use, doubles as a 5-gallon jerry can... it exists today, and when manufactured in volume, can provide clean water for the billions who don't have it today, for only $20 billion.
The heart of the system is a filter with 15-nanometer pores. The smallest water-borne virus, polio, is 25 nanometers. Thus, no disease can get through, and no chemicals are needed to make the water completely sterile. (A similar approach is the LifeStraw, which uses a larger filter plus iodine. It's even less expensive, but Wikipedia says that it may not remove all organisms.)
Here's a TED talk where the inventor, Michael Pritchard, mixes up a thoroughly disgusting concoction, filters it, and then drinks it. Pritchard talks about the potential of the technology for disaster relief and explains how little it could cost to provide clean drinking water for everyone.
A friend of mine grew up in Venezuela, and when I would talk about nanotechnology, she would always answer with stories of conditions in developing nations, asking "What can technology do about that?" I'm glad to finally have an answer for her.
Although this isn't the first solution to be proposed for the problem of clean water, it may be enough less expensive, more effective, more independent of infrastructure, and easier to distribute and use... it may be the answer that finally inspires the world to solve the problem rather than just chipping away at it. I'll be donating and fundraising for it.