Journalist Tik Root tested the energy-efficiency of the typical approaches to boiling water, and wrote up his findings in the New York Times. Turns out the electric kettle is quite a bit more energy-efficient than either the stovetop or the microwave.
I like my electric kettle. It takes just over a minute to heat up the 0.6 liter of water (20 ounces) that I heat up on a typical day. When heating water for coffee, I do not let it reach the boiling point. My ideal temperature for water to pour over coffee in my reusable filter is considerably less than the boiling point. I think it might be about 180. I have learned to hear when the kettle water reaches the temperature I like. There’s a certain set of ticking sounds and whooshing noises that comes well before actual boiling. And I’ve read that the differential represents a considerable energy savings.
Now, if you really want to be an eco-ninja, you could boil water with a Rocket Stove or Kelly Kettle. All it takes is a handful of dead twigs or other small fuel readily available from the natural environment.