Anecdotally: last year I was riding in a train that hit someone who fell onto the tracks because the platform was so crowded. 30 minutes later, one station away, a woman lost both her legs when a train ran them over.
When I lived in Tokyo, they put platform guard walls in at many stations. They were about chest high and had sets of doors that would open before the train doors opened, and if we had them in NYC, both of those folks would have made it home without an incident.
In London, they simply close the station entrances (at street level) before it becomes so overcrowded. It can be a daily occurrence, e.g. at rush hour during a month of upgrade work on a particular line.
There is no record of anyone being killed or severely injured through overcrowding.
When I lived in Tokyo, they put platform guard walls in at many stations. They were about chest high and had sets of doors that would open before the train doors opened, and if we had them in NYC, both of those folks would have made it home without an incident.