  We construct higher dimensional quantum Hall systems based on fuzzy spheres.
It is shown that fuzzy spheres are realized as spheres in colored monopole
backgrounds. The space noncommutativity is related to higher spins which is
originated from the internal structure of fuzzy spheres. In $2k$-dimensional
quantum Hall systems, Laughlin-like wave function supports fractionally charged
excitations, $q=m^{-{1/2}k(k+1)}$ (m is odd). Topological objects are
($2k-2$)-branes whose statistics are determined by the linking number related
to the general Hopf map. Higher dimensional quantum Hall systems exhibit a
dimensional hierarchy, where lower dimensional branes condense to make higher
dimensional incompressible liquid.
