This paper studies properties of simplicial complexes for which the m-th
symbolic power of the Stanley-Reisner ideal equals to the m-th ordinary power
for a given m > 1. The main results are combinatorial characterizations of such
complexes in the two-dimensional case. It turns out that there exist only a
finite number of complexes with this property and that these complexes can be
described completely. As a consequence we are able to determine all complexes
for which the m-th ordinary power of the Stanley-Reisner ideal is
Cohen-Macaulay for a given m > 1.