This is one of the most incorrect and most often repeated 'interesting facts' from stupid 'interesting facts' spam that constantly circulates on the internet.
Echo is an effect caused by waves of sound caused by the same thing arriving at one's ears at different times, usually due to some of them having bounced off something a decent distance away, i.e. a cliff face.
The only way a sound could not echo would be if it did not bounce off surfaces. This means that if a duck's quack didn't echo, you would not be able to hear it at all.
For the sound to get to your eardrum, the sound waves have to pass up the throat of the duck, through the air, and into your ear. It would be a very unusual circumstance under which this path was a straight line. Therefore the sound must be bouncing off other surfaces on the way to the inside of your ear, including the inside of the duck's throat and bill, and your outer ear.
All sound echoes, and it echoes all the time. The only difference is that under some circumstances it is MORE noticeable. Thus the difference between yelling in an empty warehouse and yelling in your living room. The empty warehouse just provides lots of big flat surfaces for the sound to bounce around evenly.
I'm glad we cleared that up.
Addendum: There is another way in which a duck's quack could 'not echo'. If the duck's quack was a 'different kind of sound' which moved faster than the speed of conventional sound, it might bounce off all the surfaces en route to your ear so fast that no discernable echo could be heard.
However: Anark points out that if the duck could do that, it would emit a sonic boom. Wa-hey. But it gets better. Since the speed of sound in a given medium is constant (pitch varies with frequency) the duck's quack itself could never be supersonic (by definition!). However if the duck itself was flying awfully fast...
As Winston Churchill once said: "Not bloody likely."
endiku would also like to add that it's possible that different surfaces might absorb different sounds in different ways. So your eardrum might vibrate properly to the frequency of a quack but the hard surfaces off of which echoes might bounce just absorb it and turn it into heat energy.
It's not actually true, but it's a nice idea.
Second Addendum: As an aside, I have heard a duck's quack echo. If that's not good enough for you, go get a duck, take it to a large room with lots of flat surfaces, and squeeze it hard. Then you can also determine whether PETA's billyclubs echo when they're bouncing off your skull.
Extra Special Super Sparkle Happy Funtime Addendum: Roninspoon Edition: I suppose it's potentially possible, and I suspect this is the assumed basis of the myth, that the noise of a Duck's echo modulates across several frequencies and manages some sort of wave cancellation. I think that's crap, but I suspect that's what the scienticians at Fox Broadcasting would have us believe. They are evil and although amusing, spread misinformation.
OldMiner tells me that this is how active noise cancellation devices work. This doesn't mean it works for ducks, just that if they were sufficiently technologically advanced, it could. Or something. I remember an old Sierra adventure game called Codename: Iceman which involved a submarine with this kind of technology. I sorely doubt they used ducks in the research process, and if they did, it wouldn't have gotten them very far.
Holy Crap, It Gets Better, My Ears Are Bleeding From How Many Replies I've Gotten About This Writeup, Special Morning Price For You Addendum: Fieari informs me that there was a recent episode of a TV show called Myth-Busters which determined that a duck's quack does echo, but that in most circumstances the echo sounds so much like the initial quack that it's almost indistinguishable from the original. Basically, it sounds like the quack and the echo thereof are a single long quack. I guess this means that you'd need to be in a place with a flat, hard surface FAR ENOUGH AWAY that there was a better delay between the quack and its echoey compadre.
What I like best about this suggestion is that it actually implies that not only does a duck's quack echo, but it echoes REALLY REALLY well.