This might be recency bias, but I'll put 2014 up there.
3 first round game 7s, including the Kings 3-0 comeback vs the sharks, and a great game 7 between minnesota and colorado in OT.
A great 2nd round where 3 of the 4 series went seven games, including a classic Montreal-Boston series where Subban and Lucic took full stage. The end of Selanne in the NHL with Kings-Ducks. And the incredible Rangers-Penguins series down 3-1 where MSL's mother passes away and the rangers rally for 3 straight wins, with his mother's day goal being surreal in game 6 and lundqvist being a god in game 7.
2 good conference finals despite Price being hurt in game 1, Lundqvist being amazing again, but the real story was out west. The 2014 WCF is probably my favourite playoff series post 2004 lockout.
Hawks win game 1, then the Kings win 3 straight. This led to games 5-7 which in itself were just unbelievable. Game 5 where there 5 minutes of overtime straight with no whistles at all. Games 6 and 7 were back and forth affairs with game 7 in OT on a strange bounce.
The finals albeit only in 5 games had 4 one goal games, and 3 overtime games.
Rangers blew three 2 goal leads in game 2 and lose in OT.
And then game 5, where it went into double overtime and the kings won on a Martinez shot. That overtime was my favourite clinching game OT in a while.
It isn't as historical as 1993, but 2014 is up there in terms of entertaining playoffs with the storylines involved.