guitars

In my experience, I only run into issues if multiple devices are on different circuits of the main AC grid.

So if I have my amp plugged into an outlet that goes to one circuit breaker, and my pedal power supply plugged into a different outlet on a different breaker, there's noise. My guess is that there's a slight differential between the grounds of the two circuits. Unless there's a ground lift, most equipment joins together the grounds on the input, output, and power. So if the grounds are at slightly different charges then you get a voltage from one to the other, which causes the noise.

Practically speaking, just putting all your pedals and amps into one surge protector fixes this. Unless you have some really weird tube pedals or something, pedals have a negligible amount of power draw.

The other benefit of an isolated power supply is if a pedal has a momentary large power draw. Quality pedals have an input capacitor (basically a reservoir for electricity that deals with small irregularities), so that shouldn't be a problem, but with older or cheaper pedals it's a possibility.

If you run into noises or dropouts, try using a 9v battery instead. You can even get a real cheap adapter if a pedal doesn't have a battery compartment. If that fixes it, you could just use a cheap power supply and deal with batteries for any live gigs. Depends on how often you gig, how many pedals you use, etc.