Why is $0 \,\mathrm{K}$ so special? I know that $0 \,\mathrm{K}$ cannot be reached, this is discussed here and here.
But, why is it such an important statement? 
I mean, there are many properties which will never be zero, like: acceleration, torque, force, etc. But these facts are almost never discussed. Is it because the  absolute temperature has stronger implications?
 A: As the comments have mentioned, acceleration, torque and force can all be zero, but the key point is that some zeros are more fundamental than others.
Take acceleration: you state in a comment that Newton's law of gravity has an infinite range so the force/acceleration generated by some gravitating body can never be zero. This is quite true, but acceleration/force can be positive or negative so two non-zero accelerations can sum to zero. This is what dmckee means in his comment. Even though the gravitational fields of the Earth and Moon are infinite, somewhere in between them is a point where the net force is zero.
But (ignoring some technical definitions) you can't have a negative temperature. So I can't take a chunk of matter and make it's temperature zero by mixing it with another chunk of matter that has a negative temperature. The only way I can cool my chunk of matter is by putting it in contact with something that is colder, but of course still has a positive temperature.
So 0K is special because there is nothing colder than it.
