Electrical items that hum commonly include any device with a speaker (stereo, radio, TV, computer (including external or monitor speakers); any device with a transformer or charger (doorbell, computers, computer monitor, iPod/MP3 player, cell phone charger, etc); bathroom or ceiling fans that might be on but might have had the motor shaft come disconnected from the fan so you only hear the motor running. Also, most household fan motors are current-limited - meaning if the fan jams with lint or debris or the motor freezes up, the current will still run through it and cause a noticeable hum, but may not actually short out or burn out for some days.
A totally different, and in my experience more likely source, is your heating system - either the fan on a forced-air heater, the pump on a hot water baseboard system, or a basement or garage heater fan. Air conditioner and humidifier / dehumidifier are also possibles. All these can hum as bearings get old or as pumps get worn.
Best way to check for the source of a hum is get yourself a common stethoscope (a real one with solid metal pickup head, not cheap plastic one) for about $10 at a drugstore or box store and start holding it against heating ducts or pipes, water pipes, walls, appliances, etc - being sure not to get it into anything electrical, of course. Usually you can track down where the hum is loudest in 5 minutes or less. Once you think you have isolated it, then you should be able to turn the device off, unplug it, or turn off the appropriate breaker so it is deenergized, to be sure that is the source.