During the last sixteen years, the NHL has had one franchise move (unless you want to count the Islanders upcoming move from one part of the NY area to another part of the NY area), and the franchise that moved didn't even exist until 1999--and most of the city, Atlanta, probably never knew it existed in the first place.
Unlike in the NFL, no historic NHL franchise has moved since the 40s. The Leafs, Canadiens, Rangers, Bruins, Red Wings, Blackhhawks have all remained in their respective cities. Newer franchises with good history like the Blues, Flyers, Islanders, Sabres, Penguins, Canucks, Flames, and Oilers have never moved.