The exact answer depends on the paper. The important factor being the width and the size.
The basic idea is that each time you fold a paper in the middle, you double the layers. After one folding you have 2, after 2 foldings you have 2*2, after three 2*2*2 and so on. After n foldings you have 2^n. The point is that this is an exponential increase with grows very, very fast. E.g. 2^10 is approximately 1000.
If you start with a paper that has a thickness of, say 1/10 mm, you are already at a 10 cm pile. The problem is then that the outer sheet can't be folded anymore in the middle but has to be bend around (try it, you'll see what I mean). If the paper is too small, this just doesn't work any more.