Classic NHL rivalries withstand the test of time. Even today, the Montreal Canadiens and Boston Bruins despise each other based on ancient history from their time as Original Six franchises.
Other rivalries are formed through proximity, like the Pittsburgh Penguins and Philadelphia Flyers or New York Islanders and New York Rangers.
But in the modern-day NHL, it's playoff familiarity or frequency of divisional play that breeds the kind of contempt needed to pit teams and their fanbases against each other and make that game more important than others on the schedule.
So while old rivalries exist and may never die, new ones are forming constantly.