The R script below tests whether a set of points on a plane is significantly clustered (as opposed to randomly distributed or, conversely, equally spaced), using the Clark-Evans R measure. From the R spatstat package manual "[Clark-Evans R] is the ratio of the observed mean nearest neighbour distance in the pattern to that expected for a Poisson point process of the same intensity. A value R>1 suggests ordering, while R<1 suggests clustering."
If you have points on a sphere you'll have to reproject - as far as I can tell there's no way to use spherical distance formulas. You'll also want to use a different measure to check for spatial clustering with respect to an attribute of the data points, for example Getis Ord G.
The spatstat package requires a window (essentially a polygon bounding box, and in this example a shapefile of the contiguous US is used. Because the edges of the data are a coastline (i.e. physically significant rather than an arbitrary data limit), I'm not using the edge-correct R in the results. The test gives a p-value, which tells you how significantly clustered/ordered your data is.
install.packages("spatstat_1.31-1.tar.gz", repos = NULL, type="source")