XStar is a Unix program that simulates the movement of stars. It starts by
putting a bunch of stars on the screen, and then it lets the inter-body
gravitational forces move the stars around. The result is a lot of neat
wandering paths, as the stars interact and collide.
Along with the program, there is a fairly large document that explains the
N-Body problem in a fair amount of detail. It doesn't get into the gory
details of the "real" N-body solvers, but it does give you an overview of
the techniques they use.