Denis Potvin of the Islanders celebrates with the Stanley Cup Trophy...

Denis Potvin of the Islanders celebrates with the Stanley Cup Trophy as teammate Butch Goring waits his turn to hold the cup after the Islanders defeated the Flyers in Game 6 of the 1980 Stanley Cup Finals on May 24, 1980 at Nassau Coliseum. Credit: Getty Images/Bruce Bennett

The Islanders embark this week upon their 25th playoff appearance since entering the NHL in 1972 and the organization does have a storied postseason history.

Just not recently, of course, with one playoff series win since 1993.

But beyond the four Stanley Cups from 1980-83 and 19 straight playoff series wins, there were nearly yearly battles with the rival Rangers, an epic run in 1975, a surprise run in 1993 and brutally physical series against the Maple Leafs in 2002 and Capitals in 2015.

How do the playoff runs rank? Here’s how Newsday sees it:

1. 1980: Stanley Cup champions.

The first is always the best and Bobby Nystrom’s overtime goal off John Tonelli’s feed in the decisive Game 6 of the Cup Final against the Flyers at Nassau Coliseum is as indelible a moment as the franchise has ever had. For Islanders’ fans, it’s their Bobby Orr flying across the goalmouth after his overtime Cup winner for the Bruins in 1970. The Islanders won 15 of their 21 playoff games, never faced elimination or trailed in a series and Bryan Trottier won the Conn Smythe as the playoff MVP. Not to be overlooked: Ken Morrow, fresh off the Olympic Miracle on Ice, scored the overtime winner in Game 3 of the best-of-five first-round against the Kings with that series tied at one game apiece.

2. 1983: Stanley Cup champions.

The Islanders raised the Cup one last time at the Coliseum, sweeping the Oilers in the Cup Final to delay the onset of Edmonton’s dynasty by one year. Mike Bossy scored 17 playoff goals for the third straight postseason and goalie Billy Smith won the Conn Smythe. The Islanders lost just five of 20 playoff games and, again, never faced elimination.

3. 1981: Stanley Cup champions.

The Islanders lifted the Cup at the Coliseum for the second straight year with a Game 5 win over the Minnesota North Stars. The Islanders were as dominant as ever, winning 15 of 18 playoff games, including a semifinal sweep of the Rangers as they scored at least five goals in each victory in that series.

4. 1982: Stanley Cup champions.

The Islanders struck a blow for fashion by sweeping the Canucks and their colorful “V” jerseys for the Cup with Bossy winning the Conn Smythe. To get there, the Islanders needed Tonelli’s overtime goal against the Penguins in the decisive Game 5 of the first round after losing two straight at Pittsburgh.

5. 1975: Lost in semifinals.

Other than a Cup, this playoff run had everything. The upstart Islanders eliminated the veteran Rangers, 4-3, in the decisive Game 3 of the first round on J.P. Parise’s goal 11 seconds into overtime. The Islanders then rallied to oust the Penguins with a 1-0 win in Game 7 on Ed Westfall’s goal after dropping the first three games. The Islanders also lost the first three games of their semifinal with the eventual Cup champion Flyers before forcing a Game 7, which they lost 4-1.

6. 1984: Stanley Cup finalist.

The dynasty finally ended as the Oilers needed just five games in the Cup Final to snap the Islanders’ unapproachable record streak of 19 straight playoff series wins. But the Islanders’ championship pedigree did allow them to rally from two games down to beat the Rangers in the first round on Morrow’s overtime winner in the decisive Game 5 and then beat the Canadiens in the conference final in six games after losing the first two.

7. 1993: Lost in conference finals.

The Islanders finished third in the Patrick Division at a so-so 40-37-7. But they beat the Capitals in six games, including double-overtime wins in Games 2 and 4 and an overtime win in Game 3, then eliminated the two-time defending Cup champion Penguins in seven games on David Volek’s overtime winner before bowing to the eventual Cup champion Canadiens in five games in the conference final. Who knows what would have happened had the Capitals’ Dale Hunter not separated Pierre Turgeon’s shoulder as he celebrated a Game 6 goal in one of the dirtiest hits in playoff history.

8. 1987: Lost in division final.

The Easter Epic, the longest Game 7 in NHL history, defined this playoff run. Faceoff was on Saturday, April 18. But it was 1:58 a.m. on Easter Sunday when Pat LaFontaine’s slap shot sailed over the glove of Capitals goalie Bob Mason at 8:47 of the fourth overtime, completing the Islanders’ comeback from a 3-1 series deficit in the first round. The Islanders nearly did it again in the next round, rallying from a 3-1 series deficit against the Flyers before losing, 5-1, in Game 7 at Philadelphia.

9. 1977: Lost in semifinals.

The young Islanders continued to build their championship foundation, finishing with 106 points and sweeping the Blackhawks in two games in the first round and then the Sabres in four games. But the Canadiens, who won four straight Cups from 1976-79, won three of the first four games. The Islanders did stave off elimination with a 4-3 overtime win in Game 5 before bowing, 2-1, in Game 6.

10. 1976: Lost in semifinals.

The Islanders surpassed 100 points in the regular season for the first time, easily dispatched the Canucks in two games in the first round, then rallied to beat the Sabres in six games after losing the first two games. The Islanders were eliminated by the eventual Cup champion Canadiens in five games, losing the first three games by a goal apiece.

11. 2016: Lost in conference semifinals.

Now playing at Barclays Center, the Islanders positioned themselves to play the Panthers in the first round and won their first series since 1993 in six games as John Tavares tied Game 6 in Brooklyn with 54 seconds left in regulation and scored the winner in the second overtime. The Lightning then eliminated the Islanders in five games.

12. 2002: Lost in conference quarterfinals.

The Maple Leafs won the first-round series in seven games – the home team won each game – in a nasty series. The Islanders lost captain Michael Peca and defenseman Kenny Jonsson on questionable hits in Game 5 but Shawn Bates’ penalty shot goal in Game 4 is one of the Coliseum’s iconic playoff moments.

13. 1979: Lost in semifinals.

This was supposed to be the year after the Islanders led the league with 116 points. They swept the Blackhawks in four games but the underdog Rangers shocked them in six.

14. 2015: Lost in conference first round.

This was supposed to be the Coliseum’s final NHL season and the Islanders used home ice to extend their series against Barry Trotz’s Capitals with an emotional 3-1 win in Game 6. But the Capitals closed out an overly physical series with a 2-1 win in Game 7.

15. 1978: Lost in quarterfinals.

The Maple Leafs shocked the Islanders and goalie Chico Resch with a 2-1 overtime win in Game 7, the first road victory for either team.

16. 2013: Lost in conference quarterfinals.

The Islanders battled the Penguins through an electric first-round atmosphere at the Coliseum but were ousted, 4-3, in overtime in Game 6 at home.

17. 1985: Lost in division final.

The Islanders rallied for a five-game win over the Capitals in the first round after two overtime losses, but the Flyers eliminated them in five.

18. 2007: Lost in conference quarterfinals.

The top-seeded Sabres ousted the Islanders in five games in the first round, though three of the last four games were decided by one goal.

19. 2003: Lost in conference quarterfinals.

The top-seeded Senators eliminated the Islanders in five games in the first round and then-GM Mike Milbury hastily reacted by firing future Cup winner Peter Laviolette, who led the Islanders to the playoffs in each of his two seasons after they had gone seven seasons without qualifying.

20. 1988: Lost in division semifinals.

A huge disappointment. The Patrick Division-champion Islanders lost in six games to the Devils, making their first playoff appearance since relocating to New Jersey and with Lou Lamoriello in his first season as the team’s boss. It was the last time the Islanders had home-ice advantage in a series.

21. 1986: Lost in division semifinals.

The Capitals swept the remnants of the Islanders’ dynasty in three games in the first round.

22. 1990: Lost in division semifinals.

The Islanders’ lone win in a five-game, first-round loss to the Rangers came in double overtime in Game 3.

23. 2004: Lost in conference quarterfinals.

Steve Stirling’s first season as coach ended with the Islanders shut out three times in a five-game, first-round loss to the eventual Cup champion Lightning.

24. 1994: Lost in conference quarterfinals.

The Islanders were outscored by an aggregate 22-3 in a four-game, first-round sweep by the eventual Cup champion Rangers.

The 1979-80 Islanders

Record: 39-28-13, 91 points

Finish: Second place, Patrick Division

Playoffs: Preliminary round – Defeated Kings three games to one; Quarterfinals – Defeated Bruins four games to one; Semifinals – Defeated Sabres four games to two; Stanley Cup Final – Defeated Flyers four games to two

Award winners: Bryan Trottier, Conn Smythe (Playoff MVP)

Statistical leaders: Mike Bossy (51 goals); Bryan Trottier (62 assists, 104 points)

Goalies: Chico Resch (23-14-6, 3.04 goals-against average, .901 save percentage); Billy Smith (15-14-7, 2.95, .899); Richard Brodeur (1-0-0, 4.50, .829)

Hall of Famers: Coach Al Arbour, right wing Mike Bossy, left wing Clark Gilles, defenseman Denis Potvin, goalie Billy Smith, President/General Manager Bill Torrey, center Bryan Trottier

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