A wise man once said that the root of all evil is in fact the power supply. This is especially true with audio equipment where power supply issues can propagate almost directly to the output. Digital audio has certainly made the situation better, as even a noisy, misbehaving power supply can be masked by the better noise immunity of digital systems. While digital audio is not completely removed from the effects of bad power, it is unlikely that a linear supply with excessive ripple will cause hum in the audio.
Classifying power supplies into two broad categories of linear and switching will help shed some light onto potential issues. A linear supply is normally based upon a traditional step down transformer, an AC to DC rectifier, regulation, and output filtering by virtue of large capacitors. A switching supply modifies the width of pulses in a high frequency pulse train for voltage regulation and the result is filtered by smaller capacitors, thanks to the higher frequencies employed.
The good thing about linear supplies is its simplicity and thus its reliability. The bad things include size, weight and heat due to their relative inefficiency. Linear supplies can also be less effective at blocking noise from the AC power source feeding their inputs, meaning that the noise can be present within the rest of the equipment and can possibly be transferred to audio outputs.
The good thing about switching supplies is their efficiency. Bad things include complexity, noise injected back into the AC power line feeding them, and high frequency noise on their DC outputs that can possibly be transferred to audio outputs as well.
All equipment has two common things: a ground and the power supply. Both must be carefully considered to produce the best possible performance from the gear.
