There are several ways to transfer energy through long distances of hard vacuum and even the atmosphere wirelessly. What Nikola Tesla was doing back in the pioneering days of wireless power wouldn't really work, because electrodynamic induction transfers lose too much of their efficiency over distances much larger than one sixth of the wavelength. And accounting for atmospheric resistance, these distances should probably be even a lot shorter.
But short of actually transporting stored energy physically in charged galvanic cells (i.e. batteries) even if those came at far greater than currently achievable capacity per their mass, maybe by using carbon nanotubes as charge carriers similar to what is currently being developed for mobile applications, or even transporting charged plasma, all of that would most definitely incur net loss in required energy to establish such pathways compared to gains in transported energy. So here are a few other ways, with no transport required (short of building the transmitter and receiver end, of course):
Microwave: Powerful microwave wavelength radio transmitters could be orbited in GEO (Geostationary Orbit) and target a ground based rectenna (rectifying antenna) that would convert microwave energy into direct current electricity.
Problem with this approach is, that the diffraction is too great due to interference pattern forming at the transmitter end increasing the radius of the receiver end with distance and angle of diffraction. The shorter the wavelength however, the smaller the required size of the transmitter and the rectenna, their required size ratio, and lower absorption and refraction of the microwave beam in the atmosphere. The biggest problem however is with the required rectenna size increasing by the distance from the beam's source, so while GEO sounds simple enough in terms of targeting a particular area on the surface, it is too far away and would require an enormous size collector, and stationing the transmitter in lower orbits means you'll have targeting problems. A bit off, and you'll either be scorching its surroundings if the power density is too high (see: feasibility*), or you'll require too big rectenna to lower power density to human safe levels (1 mW/cm2).
So while this method of transmitting wireless power might be used for some other space applications, maybe from orbits of less massive celestials, preferably with less dense atmosphere, between space stations or to power up satellites wirelessly, i.e. it is feasible for shorter distances or through hard vacuum alone, Earth based rectenna targeted by a satellite in Earth's orbit simply isn't. As much*. Quoting Wikipedia, for a station that would transmit 750 megawatts of total power (one modern electric power plant's worth of power), a 10 km diameter receiving array would be needed to transmit human safe power density to Earth.
Laser: This is far more feasible for Earth orbit to Earth (earthbound) application, or indeed the other way around, Earth to Earth orbit (space bound), than microwave wavelength electromagnetic radiation due to narrower beam requiring a smaller receiving photovoltaic cell array radius per distance, but suffers higher atmospheric refraction and with it loss in efficiency, power conversion rates are far smaller (best of class photovoltaic cells achieve up to 50% efficiency, and they are terribly expensive to manufacture) and you end up with a death ray scorching the Earth beneath it, if the targeting is off by a tiny amount at the transmitting end.
Cloud cover is also a big problem for laser solutions, increasing atmospheric absorption and scattering to the point of infeasibility. While converting electricity into a laser beam might be highly efficient and relatively easy to achieve at the transmitter end, it would be almost impossible to provide continuous power with all the atmospheric formations obscuring the beam.
Solar concentrators: Earth orbit stationed parabolic mirror or fresnel lens based solar concentrators could be used to focus a narrow beam of the total spectrum solar concentrator towards the Earth based solar thermal collector, and either convert its power to electricity, or additionally concentrate captured beams into a narrower spot and use its energy to power a solar furnace.
While I honestly haven't a clue as to how narrow of a spot one could achieve by using optics alone over such distances, I presume it could be narrow enough to be perfectly feasible, given proper atmospheric conditions. With dynamic spot focusing, it could even be used to disperse cloud cover first, then refocus to an Earth based total spectrum solar concentrator and do that continuously, if cloud cover is on the move (which it usually is). Of course, you really wouldn't want to miss your target with this highly concentrated sunbeam when its focal length is close or equal to its source distance from the surface of the Earth.
All of these methods require a direct line of sight and are affected to varying degree by atmospheric absorption and scattering. Not just the cloud cover, but also fog, pollutants, even pollen count. Microwave and laser links are however perfectly acceptable for long distance communication needs (magnitudes less powerful transmissions than power beams), but our own planet's environmental constraints make wireless transmission through the atmosphere infeasible* and couldn't provide continuous power without relaying it through several satellite transmitters and ground based receivers, with each transfer decreasing the total system's efficiency.
For in-space application though, with no atmosphere in between to negatively affect your power transmission efficiency, sure. All of these methods would work, as long as the distances aren't too great to require too large collectors.
Has this been done before?
Yes. It is believed that the anti-ballistic missile (ABM) testing range in Kazakhstan, named Terra-3 and built by Soviets in the late sixties was (on top ABMs) using a laser directed-energy weapon powerful and accurate enough to disintegrate or at least completely damage targeting electronics of Intercontinental Ballistic Missiles (ICBM) in flight, before they would get the chance to hit their targets. If they were really powerful enough to do that remains a mystery, and this laser array might have only been used for tracking, but according to the report on the Okno (Window) and Krona (Crown) Space Surveillance Sites (multilingual PDF, including English translation):
On 11 October 1984, the US defence secretary reported to the president
that equipment on the Challenger shuttle [STS-41-G] broke down
[malfunctioned] and crew felt unwell when it passed over Lake
Balkhash, near Norak, suggesting that the Soviets were testing a new
anti-satellite weapon. Indeed, the Terra-3 experimental laser radar
was used on Defence Minister Dmitriy Ustinov's orders. After a US
protest, the Soviets promised not to use it against manned spacecraft.
Dmitriy Ustinov later that month contracted pneumonia and died two months later. This incident is similarly reported in other media, but if true, this would clearly show capability of transferring large power density energy beam (laser) through the Earth's atmosphere and into Low Earth Orbit (LEO).
For tracking, measurements and communication purposes however, similar but with smaller power density was done multiple times, for example with the Lunar Laser Ranging Experiment all the way back in 1962 aiming at retroreflectors planted on the Moon during the Apollo program with Earth based lasers.
Similarly, but for communication purposes, Lunar Atmosphere and Dust Environment Explorer (LADEE) that just successfully entered lunar orbit uses Lunar Laser Communication Demonstration (LLCD) that, quoting liked to Wikipedia page on LADEE (NASA pages are down due to US government shutdown):
...will use a laser to transmit and receive data as pulses of light,
much the same as data is transferred in a fiber optic cable, to three
ground stations. This method of communication has the potential to
provide five times the current data return, as compared to radio
frequency communication, from both LADEE and future missions. The
technology is a direct predecessor to NASA's Laser Communication Data
Relay (LCDR) satellite due to launch in 2017.
European Space Agency (ESA) also successfully demonstrated Semiconductor-laser Inter-satellite Link EXperiment (SILEX) in 2001 that will be used by planned European Data Relay System (EDRS) for space-to-Earth and space-to-space communication purposes.
All of these systems, be it for targeting, tracking, measuring or communication purposes demonstrate feasibility of laser based wireless power transfers through the Earth's atmosphere in either direction, space bound or earthbound. Of course, for such applications, power density would have to be magnitudes greater, and that comes with its own disadvantages (safety, environmental issues, cost,...) as well as advantages (lower atmospheric diffraction, i.e. effectiveness for one).
* If you're confident in your targeting not to scorch the living daylight out of the nearby populace, I guess you could up the ante and go with a high enough power density to achieve reasonable levels of effectiveness on a smaller radius area and even with mild weather formations over them. There will be much opposition, and you'd have likely unwittingly started a war with some country threatened by your newly acquired capability, but apparently, so I was corrected in the comments, that is feasible (possible to do easily or conveniently).