In cold water the most common potential failure for a regulator is a first stage freeflow resulting from water freezing in the ambient chamber and preventing the sping or diaphragm from moving back to close the high pressure seat over the high pressure orifice. This can happen even in a completely sealed or environmentally protected reg if the seal fails and/or the alcohol or silicone oil or grease used leaks out.
In warm water the most likely failure for a first stage is a worn high pressure seat. This almost always begins with a slowly creeping intermediate pressure which, over the course of a minute or two with the reg pressurized but unused, will cause a very slight freeflow as the second stage vents the excess intermediate pressure. These are almost always discovered on the dive boat if you pressurize your reg a few minutes before starting the dive and then listen for a slow leak at the second stage.
It normally takes a few to several dives for the seat to wear enough to cause a freeflow between breathes in the water so you have to have ignored your reg for several dives or have a rental reg used by an ignorant diver for several dives to encounter this. It will cause an increase in air consumption but not catastophically so, and a normal ascent and safety stop is still easily done.
The most common failure for a second stage is a worn low pressure seat causing a slight freeflow. This is the most common "problem" noticed by divers as the symptom is the same as with a worn HP seat, so the diagnostic process has to start with the first stage to ensure the IP is stable before blaming the problem on the second stage.
Most other failures fall into the category of cracked cases, old case o-rings, torn mouthpieces, holed diaphragms, or folded exhaust valves that can cause the reg to breathe a bit wet but generally still allow you to get air from the reg. In any event, it's one of the reasons you have the octopus.
A second stage failure that results in a failure to deliver air is very rare and is virtually always due to an obstruction (rocks or ice) that prevents the lever from moving enough to open the poppet.
Hose failures due occur, but they almost always give you ample warning first. An HP hose will start bubbling like an airstone long before it fails. Occassionally if the cover is still perfect, you will get a big blister on one that then also leaks. In the event a knife weilding buddy attacjs you and cuts the hose, there is a restrictor in the first stage HP port that prevents rapid air loss so a normal ascent and even a safety stop will be possible.
Low pressure hose failures are potentially more serious as LP hoses are designed to flow large amounts so air and a total hose failure can empty a tank in not much more than a minute. But again they virtually always give you signs such as weather checked covers, cuts and leaks near the fittings. Pulling back your hose covers now and then to inspect the area near the metal fittings will usually reveal a cracked or cut cover long before the hose fails. A small stream of bubbles virtually always precedes a major failure by at least several dives, so they should be caught during a bubble check or observed by your dive buddy. So again hose failures are virtually always the result of poor maintence and inattention to the warning signs. If your hose covers are too snug to easily pull back for inspection, get rid of them.
Tank and valve related failures are also relatively uncommon. I have seen a few tank neck o-rings with minor leaks but I have never seen a catastophic tank neck o-ring failure. For this to occur, it needs to extrude and for that to happen the valve needs to be loose so this occurrence is a poor maintenence issue, not a design problem.
Similarly, extruded tank valve o-rings are very rare as well and are almost always the result of the yoke or DIN fitting not being tight before the reg is pressurized. If it is too loose it will fail and leak immediately. If however you are in the very narrow range between too loose and just tight enough, it may hold long enough to fail during the dive. But again this is almost always the result of operator error, not the fault of the o-rig or valve/yoke/DIN design.
The burst disc in the tank valve is designed to burst at 90 to 100 percent of the tank's hydro test pressue. This would be 4500 to 5000 psi for an aluminum 80 so it is very unlikely in normal use. But burst discs do flex with each cycle and they can become weak over time. If left in service long enough they will eventually fail at the normal service pressure. The odds are that this will occur during the tank fill or shortly after the tank is filled. It is very unusual for this to occur during a dive. Out of the water, you will hear a loud pop and a very loud and continuous screeching/whistling sound as the air escapes through the burst disc plug. Underwater you will get lots of bubbles and will need to start an immediate ascent. But this is again a poor maintence issue and if the burst disc assembly is changed every 5 years when the tank is hydro tested, it is extremely unlikely that you will ever see one fail.
Regs "blowing up" are almost unheard of. Where it can occur is if you are using a non )O2 clean first stage with very high percentages of Nitrox (50%-80% or with pure O2. The dirty first stage provides the fuel but ignition also requires a heat source and in nearly all cases this is supplied by the diver turning the valve on suddenly causing rapid compression and heating in the reg as all the gas in motion comes to a sudden stop. Even then an explosion is extremely unlikely and the most common non O2 clean event is a flash fire in the reg that chars the o-rings and causes a very obvious leak. The diver is often unaware a fire ocuured at all until the reg is dissasembled for service. Turning the valve on slowly with the purge button depressed will prevent the problem even in very dirty second stages so the issue is again poor maintence and operator error.