What is the effect called whereby people don't offer help when in a crowd because they assume someone else will help? If you are in a crowd and you hear someone call for help you assume that someone else will deal with it. If you are alone and you hear someone call for help you go and help them. What is that effect called?
It's called the bystander effect:


  The bystander effect, or bystander apathy, is a social psychological
  phenomenon that refers to cases in which individuals do not offer any
  means of help to a victim when other people are present. The
  probability of help is inversely related to the number of bystanders.
  In other words, the greater the number of bystanders, the less likely
  it is that any one of them will help.


It was highlighted by the Murder of Kitty Genovese, which is part of the negative image of New Yorkers as apathetic, and is therefore sometimes also called "Genovese syndrome".

The bystander effect is a sub-type of Diffusion of responsibility.