First, the teams that the Rangers have had rivalries with in the past, but presently do not. The Boston Bruins have had their fair share of mix-ups with the Rangers, and Boston-New York games are always heated in general.
However, New York has only met the Bruins in the playoffs once since 1973, and the two teams only meet three times a year. The two are rivals in the sense that they are both Original Six teams, but outside of that it’s mostly narrative.
The Montreal Canadiens watched the Rangers advance to the Stanley Cup Final in 2014 by defeating them, including Chris Kreider bowling over Carey Price.