RFID does this. A small identity chip in your dog or price tag can be powered by a transmitter within a few feet. Powering an LED this way is not practical as the amount of power for an LED is thousands of times more.
There are wireless charging pads for phones that can transmit a useful amount of power but the transmission distance must be around 1mm. So not useful for most other purposes.
Those are mostly known "AC coil" getting close a active AC coil and a non active, the non active will start
move the electrons indite because of the field inside the active coil, it's not a Radio wave(freq) but a magletical movement, of curse if we go really deep about that 2 we got many things in common .
I made a similar system in the 60s. A medium wave crystal set with a one transistor amplifier powered parasitically from a long wave commercial radio station. I used a 50 ft long wire antenna and there was precious little signal. Which is the problem, unless you have a nearbye transmitter hen it is a non starter.
In my country we got in every corner Radio telecomunication antennas (mobile network, GMS, GPRS, EDGE, HSPA, HSDPA, UMTS..etc) which they all work from 850Mhz to 2.1Ghz+ and there is also TV and Radio FM/AM waves. So I got here a lot of Radio Freq waves which I could use them 
There are great collections of beautifully made "self powered" crystal radio sets here and here.
Saw some examples and few of them need battery power, we are talking about a small device which could get Radio Waves and turn them into electricity.
The reason that this is very difficult is that an antenna for most RF sources is likely omnidirectional, so only a very small fraction of its power arrives in your direction. Furthermore, signal strength drops off as the square of distance, so the double whammy here is that even if you start with a kilowatt 1 miles away, the power is very low. By way of example, a 10 mw. transmitter may provide about 0.000000001 mw at a distance of 300 ft., reference to a "typical" receive antenna.
The closest telecomunication antenna from my house is 200m.
"Magnet motors" may be another useful thing to Google if you need something to pass the time.
O_o wut? I spend 2 days of my summer time looking everything about any kind of motor 
Bessler wheels are by far the best.
It was made to do heavy work for long periods, and in an official test it ran continuously for 54 days.
Looks like it was a mechanism like the mechanic watch, why? because ran only for 54days, after that
he should of somehow start it again.