FindGraphPartitions is very useful if one is doing large-scale linear algebra on sparse matrices and underlying methods need (or at least eprform better with) something close to block diagonal. It can also be useful for plotting graphs in two or three dimensions since it helps to cut down on edge intersections. A consequence is that a graph corresponding to a FEM-like mesh (for example) can be plotted in a way that might actually recover the original shape.

A good reference for this technology is the METIS site.

For the graph drawing aspect I think there is some mention in this TMJ article by Yifan Hu. And related.