I do plasma simulations and recently had the problem of finding the distance to the nearest neighbor for every of the particles in the simulation. Doing that naively is O(n^2) and took hours even for small test problems. Building an R-tree once and using if for nearest-neighbor look-ups brought that down to 5 minutes.

libspatialindex lacks documentation, but worked really nicely. The rtree interface in python is much friendlier.