Okay it's a long one, but it's important so bare with me - strength training is probably one of the most important aspects of preventing dance injury. Dance injuries have two main causes - some are due to flawed technique, some are due to a lack of strength, and some are due to flaws in technique that stem from a lack of strength.
Traditionally dancers, especially females, and especially in ballet, wouldn't consider strength training as a part of their essential dance training or education. Whether that's due to the believe that dance is an art, and therefore not requiring the same physical preparation of other athletic pursuits, or the fear of deviating from the perceived sylph-like ideal, any dancer not participating in some form of strength training is not only going to limit their body's physical capabilities, but more importantly expose themselves to higher risk of injury. Research has proven numerous times that dancers who supplement their dance training with strength training suffer less injuries.
Before we go any further, first let's address the most common fear raised by women (whether dancers or not) who avoid strength training:
You will not bulk up if you lift weights.