‘Accident’ often implies someone was hurt or something was damaged without anyone meaning to do it. He broke his arm by accident when he slipped on the ice.
Pro Tip 2/3
Not On Purpose
Use 'accident' to stress that something bad happened that nobody planned or wanted. She apologized for the vase she knocked over by accident.
Pro Tip 3/3
Serious Incidents
The word can be used for serious occurrences, such as car or industrial accidents. The factory was shut down after a serious industrial accident.