Opinions vary on this topic. Please do not include present areas of science that are already well-established. Instead, please consider areas of science that much less known to the public, but which offer promise of new discoveries that could change our world.
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It's impossible to say, since most research is being kept secret until it is ready to be published, for fear of having the idea stolen. However, some areas are currently in the news for possible breakthroughs. Quantum mechanics is the latest hot topic, with the potential faster-than-light neutrinos and the tentative evidence for the Higgs' boson.
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Its gotta be astrobiology or astrophysics. At the rate humans are jacking up this planet, we will need to get off this planet by the year 3000. Well, if we dont know where to go, how to get there, or how to survive, the human race will perish.
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String Theory. (M Theory)