It seems that with a coil or simple antenna it should be possible to collect energy from the background 60Hz radiation in any modern home. How much could reasonably collected at low voltages (3.3-5V)? Could it be enough to maintain a sleeping microcontroller (e.g. 1uA - 100uA @ 3.3V?)
The answer is "very little". I have also seen 10s of volts on a 1 MΩ scope probe when I touched it. However, the scope can only see that voltage because it has a explicit ground reference. The basic problem is that it will be very hard to get a large enough differential power pickup.
All voltages are effectively differential. It worked for the scope only because it was implicitly using the ground plug as the other connection it was comparing the probe tip voltage to. Getting a meaningful differential voltage from a small box is a much harder problem. To get any differential voltage at all by capacitive coupling, you need a E field gradient. That absolute value of the E field does not matter.
My knee jerk reaction therefore is that no, you won't be able to harvest enough power in a small box from stray power line fields in your house to run a microcontroller.
Anecdote: Many years ago when I was in grade school, I had a crystal radio. That is a type of radio that runs completely from the received RF power. We lived about 20 miles from a 50 kW AM radio station, and I had about a 50 foot wire antenna strung accross the back yard. With that antenna I could pick up that radio station at quite reasonable volume with headphones. I could also have the radio drive a impedance matching transformer connected to a small speaker. You could hear the radio station reasonably well if you put your ear up to the speaker. It was also great fun to annoy my brother with at night. I could leave it on, and you could sortof hear someone talking accross the room, but it wasn't loud enough to tell what they were saying and the sound was difficult to localize. Considering how relatively loud the sound was into the speaker or the headphones, there just might be enough power there to run a micro. The trick will be to convert it to a useful DC voltage without too much loss. By the way, my antenna was horizontal and the AM transmitter tower was vertical, but the long wire antenna still picked it up quite well.
Power collectable depends on distance to wiring, current split in go and return wiring (if it is all well balanced you get little leakage), size of collector coil, Q of collector ... .
I'd guesstimate that you could get a few microWatts in many cases. 1 uA needs about 5 uW so you may manage that level in many cases. I'd expect that 100 uW would be a lot harder to achieve in many cases.
It's not unusual for a scope probe with 1M input Z to show Volts of 50 Hz when connected to a person. That's liable to be capacitive coupling. If a person lies on or under an electric blanket you can get a small shock or skin "buzz" sensation if you touch eg finger of one to finger of other lightly. Apply any pressure and there is no shock sensation. That's also capacitive coupling.