Just to remain balanced on this, I did a few minutes of research. There have been several papers written on the health benefits of grounding. The large majority of them are written by the same people. In the random sample I looked at on pubmed.com, I found one commonality: lack of a control group in the study, a relatively small sample, and an unmistakable test subject bias.
Most of the studies included highly obvious and invasive grounding methods, such as sticking ground patches on the soles of the feet for 8 weeks during sleep. There was no attempt at a blind control group.
If you also look up the placebo effects on uncontrolled studies, you'll find the results of a study can be highly biased by subject expectation in whatever direction you wish. There should have been 100 or more subjects in two groups, both with identical grounding methods, but with one group actually grounded and one not. This wasn't done, so the papers presented only verify the placebo influence.
Sorry, with my cursory search I didn't find any scientifically conducted studies that support any health benefits of earthing/grounding. There is a lot of anecdote, and exposition, but not one presents any properly obtained statistical data such as you'd have to have for a drug efficacy study.
There remain serious health risks in grounding, however, including shock from ungrounded devices and injury from a fall caused by tripping over your ground wires.
If you want to avoid current flow through your body, you'd want it at the same potential as whatever it surrounds. Grounding won't always do that, in fact in most cases it won't. Any electrical field at any potential other than ground will cause a current flow to a grounded object. A grounded body will, in effect, act as an antenna to pick up surrounding fields and conduct them to ground through the body. Pretty sure that's not the intent! For safety, your body should be "floating" off ground. That way, should you encounter a field or electrified device, your body will assume the same potential as that device or field, and no circuit will be created, no current will flow.
There is far more data on other health-beneift products, collected scientifically and properly. Mangosteen juice comes to mind, there are several scientific studies on that reflecting positive effects. But even then you'll find, amid the hard data, nay-sayers and hype. The key is to read the research (the GOOD research), ignore anecdote, and then decide.