Hum or buzz is usually caused by a ground loop and is more likely when running signal to two different places (like two different amps). The potential for ground-loop hum can be reduced by plugging all of your gear into the same power outlet or power strip.
There is a simple test to check if your rig is susceptible to ground-loop hum: connect a cable between the two inputs you want to route the stereo signal to. Yes, this sounds strange, but it will not harm anything. This simply connects the grounds of the two pieces of gear at their inputs. If you get hum or buzz, you'll have the same problem with a stereo signal. As you can see—I mean hear—from this test, ground-loop hum is mainly a result of grounding differences and not the source equipment.
The simple fix is to break the ground loop using an Ebtech Hum X (or similar "ground loop breaker" device) on the AC plug of one piece of gear. For example, if using two guitar amps, use the Hum X on one of the two amps. If running to both an amp and direct, then try the Hum X on just the amp.
We like this solution more than using isolation transformers, because it in no way affects your signal. It also retains a safety ground connection. You should never completely disconnect the ground connection — this is dangerous!