There are nine teams that have joined the league within the past 25 years, starting with the San Jose Sharks in 1991-92. The other 21 teams have been playing for the last 25 years and 14 of them won the Stanley Cup in that time frame.
Two other teams, the Philadelphia Flyers and Vancouver Canucks, have been consistent playoff performers and have come close but failed to win the Stanley Cup.
Both teams have been successful.
The remaining five teams have failed to win the Stanley Cup or much of anything in the last quarter century. That qualifies them as the five least successful franchises of the last 25 years.