Well, my first guess would be that using a fuzz or distortion is amplifying hum from either the pedals or the guitar itself.
1. Try pedals on battery power. If the hum goes away, I'd say it's your pedal power source that's noisy.
2. Do u have hum bucking pickups? If not (P90's, Single coils etc) it could be the pickups receiving radiated noise. If you have the luxury, try a humbucker equipped guitar. If the sound goes away, look at improving the shielding in the guitar or consider humbucking/noiseless pickups.
3. Try swapping out leads. Some leads will have better noise rejection than others and you may indeed find one or both leads you are using is picking up noise from lighting/appliances etc.
4. Also on leads, if the hum is very loud, you might even have a broken shield connection on one of the cables. You can quickly test with a multimeter to ensure continuity from tip to tip and sleeve to sleeve.