A well drilling method can include detecting a drilling event by comparing a parameter signature generated during drilling to an event signature indicative of the drilling event, and automatically controlling a drilling operation in response to at least a partial match resulting from comparing the parameter signature to the event signature. A well drilling system can include a control system which compares a parameter signature for a drilling operation to an event signature indicative of a drilling event, and a controller which controls the drilling operation automatically in response to the drilling event being indicated by at least a partial match between the parameter signature and the event signature.