There does not appear to be many published studies backing up the theory but after having read all the personal reviews on Amazon based on the book "Earthing - the most important health discovery yet?", I'm intrigued. There are also some research studies listed on their website.
The link to the website is http://earthinginstitute.net/index.phpEarthing
The surface of the Earth resonates with natural, subtle energies. Ongoing scientific research is discovering the details as to why people feel significantly better when they connect with these omnipresent energy fields. Earthing refers to the process of connecting by walking barefoot outside, as humans have done throughout history, or sitting, working, or sleeping grounded indoors. For more than a decade, thousands of people around the world—men, women, children, and athletes—have incorporated Earthing into their daily routines and report that they sleep better, have less pain and stress, and faster recovery from trauma. Earthing immediately equalizes your body to the same energy level, or potential, as the Earth. This results in synchronizing your internal biological clocks, hormonal cycles, and physiological rhythms, and suffusing your body with healing, negatively charged free electrons abundantly present on the surface of the Earth.
I found out about this through my mother who has an acquaintance who recommended the book to her because he had been suffering with several ailments, including pain and inflammation and is substantially better after following the advice of the authors.
In theory it makes sense but I'm skeptical because although you can take the free advice and begin "earthing" without any cost or purchase involved by walking around in your bare feet in your back yard every day, they do sell products on their site which can allow you to get "grounded" via a bed pad, bands or patches... thus bringing out the skeptic in me.
It fits in with the same premise as the Paleo diet in that we have gotten so far removed from how our forefathers lived- no processed foods and walked the earth without sneakers. We rarely walk in our bare feet and are hooked into electronics constantly so I'm curious as to your thoughts. I do know one thing: for years I have said that I feel so much better in the spring, summer and fall than I do in the winter. I spend as little time as I have to outside once the cold weather shows up.

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