Make sure that all of the equipment you are using in your studio set up is being run on the same house circuit. You can determine this by using your circuit breaker box to turn off the various circuits throughout your household. Find one that is convenient, and run all of your gear off of that. Some buildings may have two or three phases of power; connecting some gear to one phase and some to another will often result in unbearable noise.
Run your equipment through a power conditioner. This will improve the sound of your equipment and regulate and protect if from dangerous spikes in current. Power conditioners are relatively inexpensive; quality items are made by Furman.
If you are using a mixer, solo each instrument to see if it is coming through a specific channel. If this is the case, disconnect that instrument from the mixer to see if the hum disappears. This instrument may have a malfunctioning power supply or short.
Eliminate rack gear one by one. Remove items from your signal path. A compressor, noise reducer, effect, etc. may be causing the noise.
Change the environment of the problematic equipment. Make sure that nothing is sitting on a metal table or desk that does not have rubber feet.
Straighten cables. Knotted and tangled cables may cause noise or may ruin the cable all together. Never run cable on the floor where it can be crushed and destroyed. Run cable neatly and as separate from other cables as possible.
Use balanced gear with balanced TRS and XLR cables. If you must use unbalanced gear, use balanced cables and a line level shifter. If you must use unbalanced cables, such as RCA cables, keep them under 10 feet long.
Record or monitor a new signal, hopefully it is hum-free!