Hard to single out one from the 90's. The first round alone produced classics year after year it seemed. Sticking with what I'm old enough to actually remember with clarity, so I'll do the 00's...
2000: Some good series, but nothing I'd call a classic. San Jose upsetting St. Louis, Jersey flipping 3-1 on Philly, and Dallas beating Colorado by a goal post were all dramatic, but I don't remember the actual games themselves being over and above in terms of entertainment value. The Finals produced two epic OT games, so that might be my pick from this year.
2001: Superb second round, three game 7's. Pitt-Buffalo is sort of a forgotten one, despite those two dramatic OT wins for Mario's Penguins. Edmonton-Dallas first round was as close and intense of a 6-game series as you'll find, four games decided in OT. The Finals were kind of ordinary for a 7-gamer.
2002: For whatever reason, this year seems more memorable than the previous two. Islanders-Leafs was the last true bloodbath the NHL playoffs produced, so it gets my vote. Colorado-Detroit was great with those loaded rosters, and I guess 7-0 in the series finale has shock value. Carolina-Toronto was also a great series with lots of OT games.
2003: Toronto-Philly was great, the blowout in Game 7 takes away a bit of the lustre though. Minnesota-Vancouver was just a crazy series, that's probably the one I'd vote for. Anaheim-Detroit might the best sweep ever.
2004: We were playing some pretty ugly hockey by this point. Lightning-Flames score too low in terms of entertainment value for me. Probably have to go with Ottawa-Toronto or Flames-Canucks first rounds.
2006: I might go off the board here...Carolina-Montreal was a highly entertaining 6-game affair. Oilers-Canes had its moments, but Carolina going up 2-0 and then 3-1 takes some of the edge off. Buffalo playing Game 7 with the Rochester Americans defense was memorable, though arguably that takes away from an otherwise great series.
2007: I guess Anaheim-Detroit or Vancouver-Dallas was the best of a rather forgettable spring. Heck, throw NY-Buffalo in there too, but none of these are classics by any means.
2008: The first round was pretty good, but things really petered out after that. Flyers-Caps, Bruins-Habs, Flames-Sharks would be the candidates here. I guess I'd go with the latter since it was always a close series; the other two saw 3-1 leads built by the eventual winners.
2009: this might well have been the best playoff year of the decade. Detroit-Anaheim, Boston-Carolina, Washington-Pittsburgh were all memorable. Even Chicago in their two series wins against the Flames and Canucks produced some great hockey. The dramatic ending in New Jersey-Carolina....Anaheim stunning the Sharks....geez you even had Washington flipping a 3-1 hole on New York and a pretty good Pens-Flyers series in round 1. Not to mention the final going 7 games....I guess this year made up for the previous two.
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As a fan of physical hockey, I'll go with Islanders-Leafs. Real hatred between these two despite them not being rivals.
That was arguably the best team the Islanders produced between the mid-80s and the present day. And for that matter, it might be the best Toronto team we've seen since 1967.