Will a stone thrown in space move forever? If I throw a stone in space, in a place where gravity is equal zero, and the space had no end, and no objects to collide with, will the stone move forward forever, because no air, so no friction? 
 A: According to Newton's first law, yes. The velocity of any object will remain constant if no forces affect it. That holds in any Inertial frame of reference (if you are accelerating by yourself, then the stone will be accelerating relative to you, even if no forces act upon it).
A: From the perspective of General Relativity, assuming we can ignore interactions with intergalatic gas and the CMB then a thrown stone follows a curve called a geodesic. In general geodesics go on forever so your stone will be moving forever, just as Lev said in his answer.
However there are circumstances in which geodesic curves appear not to go on forever. I say "appear" because future theories of quantum gravity will probably change things, but at the moment we think that a geodesic that leads into a static black hole will just end when it hits the singularity at the center of the black hole. This idea is called geodesic incompleteness.
So the answer to your question is that the stone will almost certainly go on forever, unless it hits a black hole. Even then it would have to be a static black hole because  for charged and rotating black holes the stone could miss the singularity and emerge again (into a different universe, but that's another story!).
Later: Oops, I've just seen Logan's comment and you did say "where gravity is equal to zero" so my comments about black holes don't apply. Still, I think the idea of geodesic incompleteness is interesting enough to warrant a mention.
A: I believe you are all using things you know little about to make your claim seem reliable. For example, from this simple strain of comments I have heard anything from black holes to the expansion of the universe. These things, although interesting, have nothing to do with whether or not a stone will halt after being thrown into space; the forces you have described (expansion of the universe) act upon all objects in the universe already, and therefore should be included in your initial observation. As far as black holes go, we cannot exactly pinpoint where everyone of them is, so we can surely infer that the object will eventually be acted upon by one. However, since we know not the location or magnitude of the black holes, we cannot assume the interaction will halt the object's movement. This therefore requires that black holes be taken completely out of the question.
Now, the answer to your question:
Yes, it will eventually stop, because gravity does not cease to exist in space, as derived by the formula for gravity, which employs two values, the Mass of the object and the Distance of the measurable object from another object. And, since surely there are objects in the Universe which possess both Mass and of course Distance from another object, we can assume that eventually the object will be acted upon by so many gravities (perhaps infinitely many), that eventually it will halt. 
A: Actually the stone is NOT moving just and  YOU are not moving as well. You just put the stone on a different reference frame and then ... it is not moving any longer. An ant on that stone would see YOU moving as you see the stone moving. If the question is : would that stone return to YOUR reference frame then the answer is : why would it do that? The stone has no memory and hence no potential willing to get back to your reference frame. 
The main thing is that Einstein thinking was that anything that occur should be described independantly from the observer point of view which is the complete opposite of quantum mechanics which does not consider the measured object but the measure itself (the observed point of view) which caracterize the object which exist just relatively to the oserver.
A lot of particles would hit the stone but statistically it would be hit equally from all direction and momentum so this may not affect the stone rest.
Expansion of the universe may affect it but that's another story (after some time it won't be longer a stone).
