I made some simulations of them using three.js: http://www.funcmain.com/three_body_problem
Mine are pretty much the same kind of examples as those posted here, except specifically for the case N=3.
What was the shading on the bodies for? At first I thought the bright side might be pointed towards the centre of mass of the other two, but it seems not.
I'd love to be surprised, but I suspect closed and collisionless solutions with any out-of-plane components would be newsworthy and immediately publishable.
Trivial example: What about two tiny spaceships (they're small enough that their effect on each other is negligble) orbiting a star, one orbiting in the XY plane the other in the XZ plane?