Ground loop can cause considerable currents to flow on all cables on the loop. It is not uncommon to have a voltage of 1V RMS between the earth connections of power outlets that are wired separately back to the switchboard. This small voltage, with a total resistance of perhaps 0.2-0.5 Ohm, will cause a loop current of 2 to 5 Amps, all of which flows in the shield of the interconnect. This is sufficient to cause a voltage difference across the interconnect, which the amplifier cannot differentiate from the wanted signal. An earth loop will typically inject either a 50Hz or 60Hz hum into the signal.
You might have seen the following kind of device marketed for ground loop problem solving for USA markets:

The product page boasts with the following features: The Hum X Exterminator removes unwanted voltage and current in the ground line that cause ground loop hum. This noise reduction adapter simultaneously maintains a solid, safe ground. You no longer have to run your audio signal through filtering that results in loss of volume, tone, or both. Some devices simply remove or float the ground, which is never safe! Hum X removes the ground loop while leaving the ground and your signal intact. Easy to use and completely effective!
The question what comes to my mind when I saw this is how this thing works. Harmony Central Ebtech Hum-X Review gives some interesting details how this device is expected to work:
After briefly analyzing the input to output ground connections I found this to be very similar to a galvanic isolator that is widely used in the boating communities for ship to shore power connections. It appears that there are two diodes and a 1Kohm impedance that are connected in parallel from input ground to output ground. The parallel diodes are configured back to back so that there is a 0.7volt drop in each direction. Since I could not look inside the unit the diodes are an assumption on my part? they may have used transistors configured as diodes. The potential safety hazard here, is that one or both of these diodes could fail open leaving the user with no safety ground.
Non-isolating isolator article gives information how those boat isolators work: When a boat plugs into shorepower, the shorepower cord will often make an electrical connection between the underwater metals on all the boats that are plugged in, creating a risk of galvanic corrosion. A galvanic isolator is designed to prevent this by blocking DC currents with voltages that reach as much as -1.2 volts DC. This is achieved by installing two sets of devices known as ‘diodes’, with one set installed in the opposite direction to the other. There are two types of galvanic isolator, one with a device known as a ‘capacitor’ wired around the diodes, and one without. Without a capacitor, if there is AC leakage on the shorepower ground circuit that has a voltage above 1.2 volts AC, this AC leakage will ‘bias’ the diodes into a conductive state.
Narrowboat AC Electrical systems article give the following application example for boat galvanic isolator use:

When the isolator is used for galvanic corrosion protection we want to block the DC and let the AC pass though, so the quite large capacitor in parallel with the diodes is a good idea. On audio systems ground loop protection we want to block low voltage AC, so the version without capacitor is the right one to use (there could be some very small capacitors used on audio isolators for RF protection and sometimes resistors to pass low leakage currents in case installed to system where there is no ground loop).
Elliott Sound Products article Earthing Your Hi-Fi – Tricks and Techniques article give some construction details how A High Current Safety Loop Breaker Circuit (pretty similar to one believed to be inside HumX) could be built:

This circuit example has the ground isolator between the mains power ground and audio part zero voltage line. Here the circuit the current loop breaking the loop is done with the 10 Ohm resistor, the current is now less than 200mA, and the voltage across the interconnect will be very much smaller, reducing the hum to the point where it should no longer be audible. This is how the circuits work when the potential difference over the 10 ohm resistor is lower than the voltage drop of the diodes on the rectifier bridge (around 1.2-1.4V). The capacitor will pass high frequencies (RFI protection).
In case there are is some serious ground leakage the diodes will start to conduct and pass through enough current needed to burn the mains fuse if needed without too much vooltage drop (no dangerous voltages over the isolator circuit). In the event of a major fault, one (or more) of the diodes in the bridge will possibly fail. Semiconductors (nearly) always fail as short circuit, and only become open circuited if the fault current continues and ‘blows’ the interconnecting wires. High current bridge rectifiers have very solid conductors throughout, and open circuit diodes are very rare. Use of the bridge means that there are two diodes in parallel for fault current of either polarity, so the likelihood of failure (to protect) is very small indeed.
If you plan to do any experimenting in this field, make sure that you find out the legal requirements in your country, and don’t do anything that places you at risk – either from electrocution or legal liability. Neither is likely to be a pleasant experience.
Electrical safety cannot be over emphasised. Hum is damn annoying, and everyone wants it gone. There is no good reason to sacrifice one for the other, since safety and hum-free operation can peacefully co-exist with care and the right techniques.

NEVER use a three prong to two prong AC adapter to fix a ground loop problem. These devices are meant to provide a safety ground (via the cover plate screw to a grounded outlet) in the event a three prong plug is used with a two prong outlet in USA. It is wrong and dangerous trying to use such adapter to break the safety ground connection. Also do not try to use any other adapter that breaks the ground connection (some travel adapters).