  We prove that a GIT chamber quotient of an affine variety $X=Spec(A)$ by a
reductive group $G$, where $A$ is an almost factorial domain, is a Mori dream
space if it is projective, regardless of the codimension of the unstable locus.
This includes an explicit description of the Picard number, the pseudoeffective
cone, and the Mori chambers in terms of GIT. We apply the results to quiver
moduli, to show that they are Mori dream spaces if the quiver contains no
oriented cycles, and if stability and semistability coincide. We give a formula
for the Picard number in quiver terms. As a second application we prove that
geometric quotients of Mori dream spaces are Mori dream spaces as well, which
again includes a description of the Picard number and the Mori chambers. Some
examples are given to illustrate the results.
