There is some work on energy harvesting solutions for sensor nodes. The power you can get out is miniscule, but for ultra-low-power electronics, it can be enough (say, temperature logger that uses back-scatter to transmit the information back).
The main problem is usually rectification. The way I've seen it done is using very high-impedance nodes (vitually only possible in a single-chip solution because anything on a PCB or such will have way to high parasitic capacitance), so even with these tiny powers you can get enough voltage to actually activate rectifiers and so on.
Lets just do some math to get an idea of how much power we can expect in the best case:
Look at a WiFi node (for now lets assume we use the 2.4 GHz band) - these usually have in the neighborhood of 15-20 dBm EIRP. Over 10 meters, the FSPL at 2.4 GHz is about 60 dB, which means we have -40 dBm at our receiver. That is 100 nW. So lets say we somehow manage to get 100% efficiency in the rectification, I don't think there are any commercial microcontrollers that have that low power, but there are some ASIC solutions that can pull it off, especially if you do something where you spend most of your time in sleep, and only wake up a handfull of milliseconds every few minutes.
*Also keep in mind that this assumes a always-on CW transmitter, which is not the case, so in practice you will have less power still.