Note for machine watchers: the storm-damaged crane in the news, atop One57 tower on 57th Street in NYC, is a luffing tower crane.
Here's a photo of the damaged unit, from Melania Trump:
"Luffing" means the boom (also called a jib) can be raised above the horizontal, for more agility and to avoid dangling weights over neighboring buildings.
Here's an image of a typical luffing crane from Wiki:
It looks to me from the news photos of One57's crane that a wind gust caught the boom from underneath and lifted up the free end; the boom over-centered and flopped backwards. This left the collapsed boom draped over the superstructure and counterweight, with the rest hanging off the back.
Here's a closeup of the wreckage atop the counterweight, by Anna Holmes:
The structural steel of the boom will develop fatigue cracks as it sways in the wind, but the wire ropes responsible for supporting the boom in its working position (called guys, see the generic crane in the Wiki photo above) may be partially supporting the weight of the portion left hanging off the back end.
The event must have been violent, with a lot of weight shifting sides in a few seconds, so it's a tribute to the strength of the upper, unbraced length of vertical mast (the latticed support below the cab) that the mast didn't snap off somewhere around the uppermost attachment to the building.
If there are crane experts out there, I'd be interested in their opinions on how to avoid this kind of thing. As an amateur I'd think that a safer course prior to a hurricane would have been to lower the boom to a near-horizontal position, and free to weathervane in the wind, but maybe that wasn't possible at this location.