Obviously this isn't the complete history of the two teams playing against one another, but here are some key moments in Penguins/Islanders history.
That video pretty much explains the situation. The Islanders came back from a 0-3 hole to eliminate the Penguins.
The Pens were pretty much annihilated by the Islanders in the first two games of their 1982 series. The Islanders won game one 8-0 and game two 7-2 before the Penguins decided to make things competitive. The Islanders won the series 3-2 and they went on to win the Stanley Cup for the third time in-a-row.
You probably already know what happened. If not, we go more in depth here.
The Pittsburgh Penguins have never defeated the New York Islanders in a playoff series.
Now, for some more recent history.
November 3, 2007
Al Arbour returns to coach his 1500 game with the Islanders. The Islanders won 3-2.
December 11, 2008
Petr Sykora scored his first career hat trick. Dupuis also added a hat trick of his own.
April 8, 2010
The Pens put on a show in the final regular season game at the Igloo.
February 2, 2011
Brent Johnson clobbers Rick DiPietro. That game, of course, led to this:
February 11, 2011
Just a joke of a hockey game.
April 8, 2011
The "rematch" from the brawl. The Pens won in a shootout. Not much happened, but we included the video because it mentions the Pensblog. We're losers like that.
November 21, 2011
Sidney Crosby returns.
March 30, 2013
Sidney Crosby takes a slapshot from Brooks Orpik in the face. He hasn't played since.