I've been using a Logitech trackball for two years now and they're incredibly easy to clean and don't accumulate much dirt on the surface (since they're very smooth), just a little bit on the ceramic balls that they rest on in the case. You just pop out the ball every few weeks, remove the dirt with a cloth and that's it, doesn't take more than a minute.

Tne trackball rides a couple of bearings and they do pick up scrunge. It doesn't affect tracking unless it gets to the sensor window, but you'll feel it getting progressively stiffer.