I always had to dig to find this great explanation of electrical safety by Jamie in this thread and figured it was worth putting into a resource. This will probably need an update and maybe some prettying up, but it's pretty spot on...so here it a straight copy/paste of his post #10 in that thread:
The only thing they protect is you. Which a GFCI will do better If you use them, you’ll never know that you have an electrical leak because the juice flows to the grounding probe. If you don’t have one, you feel that tingle when you put your hands in the tank especially if you have a small cut on your hand. If i'ts a dangerous level of amps (above 4-6 milli amps - not volts) the GFCI will trip instead, protecting you. With a grounding probe this will not happen. Now you know you need to isolate the problem piece of equipment and get it out. The current is still going to affect your livestock even if you have a grounding probe since they are now part of the closed circuit of electricity within your aquarium. If you have current in your tank it needs to be corrected. Stray voltage also messes with sensitive probes especially ph and salinity probes. There is a lot of debate on them I personally don't use them and don't recommend them.
Heres some cut and pasted info in different scenarios for you
Scenario 1. Hot line to water via submerged equipment. This is when a submerged piece of equipment like a powerhead, heater or UV lamp fails and the hot line of the power supply gets in contact with the water:
a) No GFCI and No Ground Probe.
As the tank is isolated from ground via plastic piping and wood stands the water becomes energized to 110 V but the main breaker does not trip as there is no current to ground. Fish has no problem because they are in a situation similar to a bird standing on a power line. This is a VERY DANGEROUS situation for the aquarist because as soon as you touch the water you get electrocuted as you become the path of current to ground. Breaker does not trip as there is not enough time for it to act or enough current to create enough heat. (They are slow trippers)
b) GFCI installed but no Ground Probe: Again nothing happen initially but the tank gets energized to 110 volts. as soon as you touch the water the GFCI will trip within 5 milliseconds and below a current of less than 5 milliamps. You may feel a small shock but nothing enough to hurt. This is the safest situation for the tank critters but may still hurt the aquarist mainly if the GFCI is malfunctioning.
c) GROUND PROBE INSTALLED BUT NO GFCI (Our case of discussion in this thread): As soon as the device fails and a short circuit is established then current is established to the ground probe, current may or may not be high enough to trip the breaker. Fish and critters will die and corals will RTN. If the breaker does not trip (Which is most of the cases) the short circuit may not be noticeable and you will be at a loss of why your critters are dying, even if you touch the water you may not notice unless the ground probe is not making a good ground. (See also Scenario 3c below) This is also a dangerous situation for potential fire. The current could be high but not high enough to trip the breaker, wires heat up, insulation melts and they catch fire.
d) Ground Probe Installed and GFCI installed: As soon as the short circuit is established the GFCI will trip shutting down whatever equipment is connected giving you a physical indication there is a short and something bad for you to fix immediately. This is the safest situation for the aquarist but has the downside that if you are away from the tank for a long time the lack of operating vital equipment may put your critters at risk.
So under this scenario the safest for the aquarist is to use both a GFCI and a ground probe. The next safest is to use GFCI alone.
Scenario 2: Short circuit between hot line and neutral on submerged equipment:
a) No GFCI and No Ground Probe: device and line will over heat. if current is high enough breaker will trip but it may take some time 10 seconds up to 5 minutes depending on the quality of the short. Plastic parts or rubber seals on the device may melt creating a secondary short reviewed under scenario 1 and releasing toxic chemicals into the water also copper wire may get exposed also releasing copper sulphate and other copper compounds to the water. Large mortality of critter is most probable.
b) GFCI installed but no ground probe: GFCI will not activate even if a secondary short to water is created as the water is not grounded and there will be no leakage current to create a current un-balance between hot and neutral so GFCI will not be able to detect the situation. Here as in 2a above (as well as 2c below) you are dependant on the breaker.
c) Ground probe installed but no GFCI: Same situation as in 2a above but if a secondary short is created current will be established killing the tank inhabitants but just probably faster than the toxic chemicals or copper compounds. Here you are dependant on the breaker.
d) GFCI and ground Probe installed: If a secondary short is created this will be same as 1d above, GFCI will trip reliving both the short circuit and disconnecting the power to the device probably preventing or reducing the damage by chemicals or copper. If no secondary short develops again you depend on the breaker.
Here again the safest alternative will be GFCI and ground probe installed although will not be effective if a secondary short to water is not established. Note that as mentioned above a short from hot to neutral may create a fire as the wires may get hot enough to initiate it.
There is a new device in the market that will replace the breaker and designed for this kind of fault. It is called an AFCI (Arc Fault Circuit Interrupter) This device will fulfill the functions of a breaker but while a breaker rely on the heat of the wires created by the short circuit which makes it slow an AFCI detects the arc on the short circuit acting immediately. For full protection under scenario 2 an AFCI in the main panel plus a GFCI in the outlet and a ground probe in the tank will provide for full protection.
Scenario 3: Short circuit from hot to a metal part of a non-submerged device and there is no current to trip the device as the metal body is not grounded: This is typical of a lighting fixture to whome one of the light bulb wires toches the reflector or the metalic hood or when some of the wiring of external pumps short to the pumps body and the body of the pump is not grounded.
a) No ground Probe and no GFCI installed: As the fault is external to the aquarium the aquarium does not get energized and no effect. If you touch the device depending on how well insulated from ground you are (rubber soles vs bare foot, globes vs bare hands etc) you may just get jolted or may get electrocuted.
b) GFCI installed but no ground probe: If you are touching the water and touch the device the GFCI will trip even if the short is within the external device. Typical of this fault is when a termial on a lamp in the hood gets shorted to the hood itself via salt creep. you are working in the water while you touch the hood with your arm or shoulder.
c) Ground probe and no GFCI: This is one of the the main reasons why probes shall not be installed unless a GFCI is also installed. The water will be perfectly grounded. If you are working in the water and touch the device you will get badly shocked or electrocuted even is you yourself are electrically insulated by the use of rubber soles or such.
d) Ground Probe and GFCI: GFCI will trip as soon as you touch the body of the device saving you once more.
For this scenario the safest will be 3b and 3d above. To make this a really safe situation: i) Use only devices installed with three prong plugs they usually ground the body using the third prong.
ii) Replace the plug and wire of any device to a three pong plug and connect the green wire to the body of the device. (The metal hood, the body of the ballast, the casing of the pump etc.)
Note that many power heads only use 2 prong plugs, if possible select one with three prongs. (Maxi jets used to have three prong wires and plugs but they were replaced with a lighter insulation wire and two prong plugs. It is still unclear to me why. Cost?, Did not want to potentially ground the water? Only they know)
Scenario 4: Short from hot to neutral or grounded body of an external device:
Under this scenario for all cases you will be dependant on the breaker. If the current is high but the breaker is slow on acting there might be a fire. The use of an Arc Fault Circuit Interrupter instead of a breaker will reduce the fire possibility.
Scenario 5: Short from Neutral to water: As usually the neutral wire is grounded either at the outside were the wires enter the house or at the main nothing happens unless this neutral grounding is not perfect some small voltage may develop creating the following situation:
a) No GFCI and No Probe: nothing will happen, you may detect small voltage of the water to ground, if you touch the water you may feel a small shock if you are not insulated enough.
b) GFCI but no ground probe: if you touch the water and the voltage is high enough to generate at least 5 milliamps the GFCI will trip.
c) Ground probe but no GFCI: The small voltage may create a permanent small current, this may be enough to start killing the most sensitive critters, (Pods and Snails) and create coral RTN over long term.
d) GFCI and Ground Probe: same as 5b above. If the current is below 5 milliamps it may still create a small current which may affect the tank inhabitants but in a lesser degree given the smaller current level than 5c above.
So in summary overall the safest for the aquarist will be the installation of AFCI, GFCI and Ground Probe. The safest for the inhabitants will be AFCI and GFCI without ground probe. This is the reason why many aquarist do not use ground probes (but will always use GFCIs) specially traveling ones that stay away for extended periods of time. If you have a remote alarm system installed that may page you or send you an E-Mail in case of a fault (Like the aqua controller from Neptune Systems) you shall have no doubts and have your Probe installed with your GFCI's)
Opposite the most dangerous situation is not having at least a GFCI. By the way many states, city or county electrical codes require installation of GFCIs on any location where electrical equipment may be exposed to water like outdoors, kitchens, bathrooms, aquariums, spas etc. If this is the case and there is an accident or fire the insurance company MAY NOT PAY. so be warned.