It is best to see a dentist soon, because it is often hard for a patient to evaluate the extent of his damage. Sometimes, a patient without much pain has sustainned a significant injury to a tooth. Fortunately, most times having your crown break isn't such a big a dental emergency. Most times when the patient is seen the crown either needs to be replaced or smoothed.
Some times the remainder of the crown is sharp and can irritate or cut the tongue.
If the underlying tooth is exposed, sometimes the tooth is sensitive to air or cold liquids. That means the pulp inside the tooth is still alive(a good thing!). Although this is anoying and can be a pain, nothing will happen to the tooth in twenty four to 48 hours. Teeth do not decay in one week. It takes time for decay to develop
Occasionally, when a patient calls and says "my crown broke", what actually has occured is the tooth under the crown has broken off and the crown has come out. This can be a bigger emergency. When the patient does come in, the remainder of the tooth has decay and sometimes it requires endodontic treatment. Often these teeth do not hurt, since the pulp is already dead. Some teeth have sustained vertical fractures and in a worst case scenario the tooth needs to be removed.