Gunsmith's answers:
Broken stocks are #1. Probably by about 6 to 7 times. Falls from loosing their footing as well as horse wrecks and rolling 4 wheelers all combine to make this the #1 thing I am asked to do repairs to, during every hunting season.
Broken extractors are #2.
Broken trigger parts or pins are #3
A "weapon's system failures" would be broken scopes but I don't classify them as gun failures. But seeing that come into my shop is about as common as #2 and #3 combined.
Others I have seen several times but not enough to give them a "rank" are broken firing pins, linkages and bulged or blown barrels.
I would imagine many end-users can recognize and replace a broken scope without the help of a gunsmith, so that may skew the data to a large degree.