The staff of the balance in your mechanical watch has pivots that are very small, and they are hardened. They sit in a shock-absorbing assembly designed to protect them, but a good whack can and does shear them right off.
The most common cause of this type of damage is dropping the watch, but it can also be from striking the watch inadvertently against a door frame, for example.
Now the above describes modern watches, but the older ones were even more fragile. Lacking any type of shock system, they are very likely to be damaged by any kind of shock, and that is why you see so many pocket watches with broken staffs. The shock systems were many and varied, but the one known as Incabloc, invented in 1934 by Georges Braunschweig and Fritz Marti of Universal Escapements Ltd., is nowadays the most common. There were many types of shock systems but they didn't show up right away in watches due to the extra cost. In a lot of brands, you don't see shock systems until the late 40's, and lower end watches still didn't have it in the 50's.
Shock protection isn't infallible- it is still possible to damage the staff's pivots, but it gives a bit of extra leeway, as the balance can actually be displaced sideways without harm to a certain degree.
Now many of you may remember the highly entertaining 'Timex Torture Tests' of the 60's, and may be wondering why they were so tough, being strapped onto water skis and thrown off bridges and other stunts.
The answer is that the design of the staff doesn't have finely turned pivots, but is a chunky rod with conical ends, that don't really break. This means that shocks will likely destroy the gears before it has any effect on the balance. It also means an increase in friction by a huge magnitude.
This was all ok, because Timexes were designed to be throwaway items, as most were riveted together and not made to be repaired. We've all seen the horrifyingly cheap watches at the checkouts or in the airport junk stores, and these take the throwaway aspect to insane lows- unknown base metals, in some cases Cadmium, and the lowest end components possible. We accumulate hundreds of pounds of these types of watches every year, and they are not recyclable. In some instances, we have detected watches that have mildly radioactive metal used in making the cases. This points to an insane lack of quality or safety control in certain countries of origin.
But I digress.
Don't drop your watch or smack it about if you can possibly help it, especially those ultra cool vintage pieces.