70stang - I have this same humming sound in my home. I hear it at night when I go to bed but I do not hear in the morning or during the day. I live in a rural location far away from any industrial or mechanical area. I have gone to different rooms and the sound is there. At first I thought it might be a car idling at my neighbors but it wasn't nor do I hear anything when I step outside.
My wife does not hear the noise but could be I am more sensitive to low frequencies. I too, am at a loss to explain this.

A long time ago I had a call with symptoms like yours, Only this one kicked in at 3 in the AM and scared hell out of the customers. They thought their house was haunted. It was hard the track down because the water picked up the vibration and carried it throughout the house. We call that sympathetic viberation. Take your hand and run it around the flat part of the flapper. Are the edges a little wavey? If so you have found the culprit. What's happening is the water seeping past the flapper lowers the water level in the tank and the ballcock attempts to compensate. In time the water seeping out and the water coming in will balance out. The ballcock can't shut off and the sound you hear is the washer vibrating against its seat. The repair is simple. Replace the flapper. A few installation tips. The linkage between the flapper and the flush lever should have 1/4" of play when the flapper's seated. The water level should be 1/2" below the top of the white overflow tube when the tank is filled. Hope this helps, Tom

In addition to Tom's advice,iIt can also be number of other things, like:

1. speakers
2. security system at main panel
3. computer left turned on
4. door bell transformer
5. icemaker
6. celiing fan
7. electrical wire over the roof
8. pool equipment from neighbors
9. hot water circulation pump
10. Refrigerator
11. Water conditioning system
12. Smoke detector
13. Any electrical device in your house
14. Sprinkler system
15. Roof vent

And more...