Since your favourite poker variation is NL Hold'em, I will address the question to that game. On the turn and the river, I agree with
reglardave's explanation, quality indeed. On the flop is where I see more checking blind at my local
casinos and this is my thinking...
Occasionally, checking blind gives you position in a hand where you wouldn't otherwise. Kind of a stretch, but while your opponent will have the last action on the hand, if they choose to make any, you can counteract, where before you couldn't. So, before they had the option of Check, Bet, Raise...where now they don't have the power to raise your bet. It works well against weaker players. The whole mind-game of checking-blind and raising is more effective then simply check-raising, at least at lower limits.
Unless you are a very strong live player with exceptional reads or in a short-stacked setting, I would not suggest checking blind on the flop with premium hands. Even if you put your opponent(s) on a range of hands it can cause some tricky situations. Most players see a check blind as weakness, so with a strong hand it becomes a very deceptive trap. But in a deep stack setting, I think it can be very dangerous especially when you do it to induce a bluff. Lets say you do it with aces out of position against one opponent...it can run you into a lot of trouble.
Scenario 1 - The flop comes j 10 9 and your opponent bets, now what do you do? Instead of finding out where you were at with a value bet (2/3 pot), now you either have to fold or make a raise for a larger amount, which commits you to a hand in a lot of situations. I don't personally like to make reads for huge amounts of money in situations like that.
Scenario 2 - The flop comes 4 5 K, with two hearts, your opponent pushes, you are either in great shape if he/she has something like AK or KQ, bad shape if they have something like K10 hearts, or horrible shape if they have 45, 44, 55. Now what if they check behind you, well now the situation you created through checking blind is reversed, and you let your opponent get a free card.
Now in a short-stacked setting, folding aces probably isn't profitable especially since players are more likely to push with marginal hands on flops where they sense weakness or with weaker drawing hands.