Only two teams in NHL history have won at least four consecutive Stanley Cups.
The Montreal Canadiens did it twice. They won five from 1955-56 to 1959-60 and then again 20 years later winning Cups from 1975-76 to 1978-79.
Montreal's dynasty in the 70's was ended when the New York Islanders created a dynasty of their own winning four consecutive Cups from 1979-80 to 1982-83.