my son (the one who now has chicken pox) experienced this during birth as well (shoulder dystocia). it was VERY scary, and even though we were at the hospital, when it was all said and done the nurses told us we were "very lucky" that he had survived (he nearly suffocated). they had to work on him for a long time after the delivery just to get him breathing...he was gray and all i could think of was that scene from E.T. where E.T. is dying and turns gray. ugh, i shudder at the memory....
they told us that most often, they must actually break the child's shoulder (or collarbone?) to get them out, and said again, that we were "very lucky" that he had not had to have that done. he was 9.5 lbs., and they attributed his shoulder dystocia to his size. (and that was at being born one full week before his due date...imagine if he'd gone to term or a little over, like most babies).
but because of it, my subsequent two children were monitored very closely during pregnancy, just to make sure they didn't get so big that we might risk the same type of event. it was so scary to me. i actually told the physicians that if they thought there was ANY chance it would happen, to just give me a c-section. but fortunately, my last two weighed in at 8.2 and 8.3 respectively, so there were no complications as far as shoulder dystocia goes. whew!
my dear cousin, on the other hand, delivered both of her babies at home, in a water tub, and didn't have a single complication. she actually wanted an unassisted birth for the second child, but i think her husband was a little too nervous to go without at least having a midwife there.
unfortunately, lots of babies are lost during delivery due to physician error, so sadly, just being at a hospital during childbirth isn't the guarantee that i definitely wish it was!
personally, i'm really glad my child-birthing days are behind me. as much as i love anticipating the event, my husband and i also always found it very frightening after having such a close call during our son's delivery.