I would hazard a guess of probably a couple of times a day at LHR..............
In my past life as a Ground Eng I experienced a couple of shear pins shearing usually due to an over zealous tuggy or a tight pushback angle, which can be quite hairy with engines running and a slippery ramp.
FYI just about all tow bars have a shear pin which is designed to shear before damage occurs to the the nose landing gear of the aircraft.
However I do recall an incident that occured to an MD80 where a solid ( non shear pin) towbar was used on an extremely icy ramp. The aircraft with park brake applied and both engines running began to slide forwards pushing the helpless towbar and attached tug backwards causing them to jack-knife , the tug eventually impacting the forward cargo door , tow bar still attached !!!
Tow-barless tractors, now that's a different story alltogether ............
