Optimal number of dimensions in multidimensional scaling
I guess it depends on your purpose. If you are doing the MDS for more heuristic purposes, then often two dimensions (or possibly three) will provide the greatest visual insight.

Also, my sense from looking at your dimension by stress plot is that the greatest gains are attained when going from one to two dimensions, that the gain from two to three dimensions is still substantial, but after that there are minimal gains.