OK - my follow-up with some more sources got chopped off after second paragraph by the Angies List system - reposting it here:
Here is another (new I think) link with a LOT of listed sources of this typeof noise, from several contributors:
One thing I forgot to mention - battery powered toys or electronic entertainment devices, including laptops/tablets/game consoles/pocket electronic games/cell phones. We had that happen once, though it was only heard in one end of the house, not all over - a toy in a toybox making a sound (trying to walk while lying on its back as I recall) went for a day or so before the batteries died - did not figure that one out until we heard the same sound some weeks later after the batteries had been replaced, and recognized the sound as being the "mystery sound".
And of course tinnitus - ringing or buzzing in the ears, though going outside in a quiet area or outside sitting in the car and NOT hearing the humming could rule that out.
One thing on the alarms - many types of alarms, especially full-house alarm systems with horns or sirens, and water alarms / power loss alarms / freezer high temperature alarms / sump pump high water or power loss alarms and those types, give off a buzzing or humming when they go off and are operating only on low battery power, or when only battery operated and either sounding an alarm or giving off a low-battery alarm but the battery is so dead that it only puts out a low hum, buzz, squeek, etc. Though a good walk-around looking for them and listening at each should rule that out pretty quickly.
I did mention roof turbine vents and solar-powered items but I don't think I specifically mentioned roof-mounted solar-powered attic vents, which could hum or whine when running.
I think I did mention insects in the linked responses - wood-chewing insects like post beetles, carpenter ants, and termites make a sound something like a hum when heard at a distance, though close to the nest (stethoscope) is actually a chewing sound from many insects. Many types of worker insects like bees also flap their wings in the hive to cool it when hot, so again a stethoscope job, listening at walls and crawlspace floors - you might have an insect nest in the stud/joist space or attic or crawlspace.
One other thing - rodents - I know from experience with an attic invasion that possums "coo" or "hum" to their babies - though not continuously obviously, and when we had a nest in the crawlspace certainly was not heard throughout the house. But maybe a louder animal like coons do.
Also - if you have a sewage lift pump system because you are down in a hole or the leach field had to be built higher than the septic tank, check if you have a sewer system alarm that is going off (like in a manhole) and maybe passing the sound through the sewer lines to the house - or just a hum from it running if on a different power panel which you did not shut off, or if on a battery backup system.
Ditto if you have a foundation perimeter french drain system with wetwell and sump pump to pump that water out - though in both those cases shutting the power off would have turned them off too (unless they have battery backup), or are powered from a different breaker panel.
One other thing that jogged my mind - I think was mentioned in the referenced links - is slow water running. In addition to very slow pipe leak as I previously mentioned, could be caused by a leak backwards through a checkvalve on the sewer system if you are on a pressure system or have a lift pump or backflow valve because sometimes the sewer lines can back up to your house - so reverse flow through a slight gap in the backflow valve could make a noise like this. Similar sound can occur at times in pressure regulator/backflow preventer on the cold water line if there is a slight flow in the water lines somewhere.
Oh - another thought - an outside hose bib leaking a touch or frozen so wateris escaping through a slight crack - ditto to sprinkler system possible leaking a bit of water through the control box.
And ditto again to water softener leaking a bit of water through the flush valve constantly, even when it is off.
Also - slight water flow from a leaking faucet or toilet outlet or inflow valve. A toilet "running" can make a number of different sounds, including humming, so check with stethoscope at toilet. Can make a noise when outflow is so low that it does not cause a disturbance in the toilet bowl water- though could eventually (depending on flowrate and how often the toilet is used) eventually cause "ghost flushes" where the inflow valve runs for a very short time to refill the slow drawdown from the leakage out of the tank. Can also be from leaking/sticking/gunked up toilet inflow valve - causing a constant very small inflow to the tank, which would usually lead to some water dripping out of the bowl refill tube (the small tube from inlet valve into the top of the overflow tube), or slow filling of the tank by the inlet valve, resulting in very minor (possibly more a "wicking" than a flow) overflow into the overflow tube, which leads to the bowl.
Not a continuous sound, but furnace exhaust fans on high-efficiency direct-vent furnaces and boilers and water heaters sometimes run for some minutes after it stops firing, some water heaters have heat pumps on top, compressors (A/C and reefer and any separate deep freeze) commonly make a humming or wheezing or whistling sound as the pressure drops off right after they shut off - but again only for a minute or so. And of course, if the power were shut off to them such a sound would diminish within a minute or two.
One other water running possibility - makeup water refilling boiler (inlet valve at pressure regulating tank operating to replace vented air in boiler) though again only for a few seconds at a time. Ditto to venting of air from a hot water/steam heating system. Continuous sound could occur if there is a leak in a radiator or pipe in a steam or hot water (hydronic) heating system, including in-floor loop heating - though eventually one would expect a leak to show up somewhere (though might be in crawlspace or wall or other out-of-the-way space).
Another possibility - leaking or slightly operating (rightly or wrongly) overtemp/ overpressure valve on water heater or boiler - slightly leaking water out the overflow pipe, which if run into a drain might not make for a visible wet spot.
Compressor leaking - though if heard through house an A/C or reefer/freezer compressor would be expected to run out of refrigerant in hours or a day or so if leaking enough to be heard like that. But a workshop compressor left turned on could be bleeding air at a hose fitting - though would be expected to kick back on periodically to recharge the tank as the pressure drops.
Ditto to a pressure tank leaking water or air - on well pump, or large surge or pressure relief tank for water heater/boiler (some of the old ones were water-heater sized ones put in the overhead floor joists). Could make noise as long as there is pressure in the system.
Ditto to leaking foot valve if you have a well pump - allowing a slight leak back into the well under pressure - could make a whine or humming sound which would carry through the pipes and water column throughout the system.
Guess I have run out of thoughts - other than maybe the Three Chipmunks have moved in and are warming up their humming to practice for a new song.
Good Luck finding it - and I would appreciate it if you could use the Answer This Question yellow button right below your question to respond back with what it turned out to be, for future info on questions like this - and out of simple curiousity.