New York Islanders

It is ancient history now, but back in the 70s, in the heyday of the World Hockey Association, this rival of the NHL made plans to put the New York Raiders, in the new Nassau Veterans Memorial Coliseum. Since many in Nassau County did not consider WHA a legitimate professional league, they scrambled to form their own NHL team to play in the Coliseum, thus resulting in the birth of the Islanders. Originally expected to be called Long Island Ducks, the New York Islanders have been the major rivals of New York Rangers ever since the 70s.
This was due largely to General Manager Bill Torrey's tactic of not hiring veterans in the Islanders' early years. Instead, he opted to steadily build a team of strong draft picks. The New York Islanders had a shaky beginning, losing its first season as the worst in NHL history, and then losing the second season, but with marked improvement. Torrey convinced St. Louis Blues coach Al Arbour to be part of the team, a move that proved, in the coming years, to be critical. Torrey also picked superstar defenseman Denis Potvin in the amateur draft.
In its third season, it made a sweeping comeback, the most impressive in NHL history, taking down a very surprised New York Rangers, and then proceeding to take down Pittsburgh Penguins in a best-of-seven match. This was legendary because the Islanders, with three games down, ended up beating Pittsburgh by winning four games in a row.