I have a very strict definition of a dynasty:
1 - A dynasty must begin by winning a Stanley Cup. Even losing Game 7 of the Stanley Cup Finals in overtime doesn't count. It must start with a championship.
2 - The dynasty must win a total of at least four Stanley Cups, in any span, as long as they make the Playoffs every year of that span. They cannot miss even once.
3 - The final year of the dynasty is the team's most recent championship.
For example, the only current dynasty is the Detroit Red Wings - from 1997 to present. The Red Wings have made the Playoffs every year since their first recent championship, in 1997, and have won four in this span. But if they missed the Playoffs next year, in 2016, their dynasty would be said to have ended in 2008, when they won their most recent championship.
1997 - 3rd in Conference, 5th in League - Stanley Cup Champions
1998 - 2nd in Conference, 3rd in League - Stanley Cup Champions
1999 - 3rd in Conference, 6th in League - Lost in Conference Semi-Finals (Colorado)
2000 - 2nd in Conference, 2nd in League - Lost in Conference Semi-Finals (Colorado)
2001 - 2nd in Conference, 2nd in League - Lost in Conference Quarter-Finals (Los Angeles)
2002 - 1st in Conference, 1st in League - Stanley Cup Champions
2003 - 2nd in Conference, 3rd in League - Lost in Conference Quarter-Finals (Anaheim)
2004 - 1st in Conference, 1st in League - Lost in Conference Semi-Finals (Calgary)
2005 - Season cancelled (lockout)
2006 - 1st in Conference, 1st in League - Lost in Conference Quarter-Finals (Edmonton)
2007 - 1st in Conference, 2nd in League - Lost in Conference Finals (Anaheim [won Cup])
2008 - 1st in Conference, 1st in League - Stanley Cup Champions
2009 - 2nd in Conference, 3rd in League - Lost in Stanley Cup Finals (Game 7 - Pittsburgh)
2010 - 5th in Conference, 7th in League - Lost in Conference Semi-Finals (San Jose)
2011 - 3rd in Conference, 6th in League - Lost in Conference Semi-Finals (San Jose)
2012 - 5th in Conference, 10th in League - Lost in Conference Quarter-Finals (Nashville)
2013 - 7th in Conference, 13th in League - Lost in Conference Semi-Finals (Chicago [won Cup])
2014 - 8th in Conference, 15th in League - Lost in Conference Quarter-Finals (Boston)
2015 - 6th in Conference, 12th in League - Lost in Conference Quarter-Finals (Tampa Bay)
Members: (must have won at least three Stanley Cups with team during dynasty reign, and not played for another NHL club during the span of those three Cups)
Kris Draper - 1997, 1998, 2002, 2008
Tomas Holmstrom - 1997, 1998, 2002, 2008
Nicklas Lidstrom - 1997, 1998, 2002, 2008
Kirk Maltby - 1997, 1998, 2002, 2008
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Mathieu Dandenault - 1997, 1998, 2002
Sergei Fedorov - 1997, 1998, 2002
Brendan Shanahan - 1997, 1998, 2002
Steve Yzerman - 1997, 1998, 2002