Every year, people magically rediscover playoff hockey and gasp, astonished, at how exciting it is. This usually happens around the time of the first triple-overtime game, and lasts until somebody wins the Stanley Cup. At that point, hockey is magically forgotten about in most of the US until it's time for the cycle to repeat. But for those few golden weeks, hockey justifiably captures the attention of those who know enough to look, and its playoff games are the most exciting of any major sport's.
There's less scoring in hockey than in the other of the Big 4. Less scoring means fewer possible outcomes, and smaller point spreads between likely outcomes. To put it another way, if playoff hockey averages 5 goals per game, the possible outcomes are 5-0, 4-1, 3-2, 2-3, 1-4, and 0-5. 1/3 of those are one goal games, which are generally pretty exciting.
Now, compare that to an NBA game, where there might be 200 points scored total. That's a lot more possible combinations, even if you filter out the ridiculous 198-2 possibilities. Simply put, there's a wider range of possible scores, and a higher percentage of them aren't going to be close.
Throw in the fact that hockey brings back sudden death overtime for the playoffs instead of their ridiculously convoluted tie/shoot out/pants off-dance off rules for games that end regulation tied, and the mystery of why playoff hockey is so much more exciting is explained.
And it doesn't hurt that the last two minutes of any given hockey game don't take an hour all by themselves.