We've talked about tractor beams before -- using some form of energy beam to pull an object toward the beam's source. When you think about it, that seems counterintuitive. It's easy to imagine energy pushing an object away. Pulling it closer is tricky.
I read about a slightly different approach in Wired this morning (it's a great article and you should check it out). This idea involves using electrons to build up a negative electrostatic charge on your target. Once the charge has built up enough -- and it doesn't have to be much -- you can fly a positively-charged probe near the target. Since opposite charges attract, the target should drift toward the powered probe.
This could come in handy for cleaning up the massive amount of space junk we've got flying around the Earth. Anyone who has seen the film "Gravity" has an idea (although not an entirely scientifically accurate idea) of how bad things could get if a satellite or manned mission were to encounter debris while traveling at incredible speeds.
There are some drawbacks. One is that the electron beam would need to be kept on the target continuously. If you turned it off, the target would accumulate other positively-charged particles and gradually return to a neutrally-charged state. It would also be a very slow process, perhaps taking months to pull an object into a higher orbit.
Considering the many objects that are lifelessly orbiting the Earth, such an approach would take a really long time, even with several spacecraft zapping electron beams like some sort of space rave. On the other hand, any approach that harnesses the fundamental forces of the universe gets the "Awesome" stamp from me.