You can't expect a simple answer to a semi-philosophical question like this. It touches directly some very deep issues that people have argued about for a long time, and still argue about.
The 'nothing' of space means what's left when all the removable stuff (atoms, etc.) is removed. So I guess the question could be whether the un-removable part still does something. Right now, it looks like it does. The expansion of the universe looks very much like it's accelerating, the way it would if space were filled with some un-removable energy density.
Is that something? Or is it just another choice of words to describe an acceleration which could just as well be taken as an independent law of nature, without saying that 'something' in space caused it?
There's very much evidence that the acceleration from the background of energy in space was once much larger. That means that it can't always be ascribed to some fixed law, and might best be thought of as due to somethingness of space.
Of course that raises another possibility. Could there someday be another change in that background? Could there someday be truly nothing in 'empty' space? We don't know.
There are other good indications that the vacuum plays an active role in physical processes that can be measured. All the elementary particles we know of have zero size (that is, particles whose sizes we have been able to measure have been found to be themselves made up of constituent pieces.
For the particles with "zero" size, we can ask what the space is like nearby these little points. It turns out that this space is seething with particles and antiparticles, popping into and out of existence (in particle-antiparticle pairs) according to the laws of quantum mechanics. These particle-antiparticle pairs do have a net observable effect on the strength of the electric field around a real particle. In each pair, the particle that's oppositely charged to the real particle is pulled inwards, towards the real particle, while the other half of the pair is repelled. This effect amounts to a "screening" of the charge of the real particle. We can tell that this is going on by asking what the strength of the electric field is very close to a particle, and finding that it is in fact bigger than might be expected if the vacuum were "empty". There are other observable effects, such as on how strong the magnetic field is around a spinning particle.
These measurements lead us to believe that these particle-antiparticle pairs are constantly being produced and destroyed everywhere, including in every bit of vacuum. You cannot remove them, so by the definition above, they are part of the vacuum.
Here's another interesting consequence of this: Nothing can escape from inside the event horizon of a block hole. However, particles and antiparticles are constantly being created and destroyed, even near the event horizon of a black hole. One of the pair can fall in, leaving the other half of the pair to fly away. This phenomenon is called "Hawking radiation," after Steven Hawking, who predicted it in the 1970's. Black holes, if they just sit in space with no real matter to fall in (that is, they are surrounded only by vacuum), will gradually "evaporate" because of all the Hawking radiation escaping.
(republished on 07/21/06)