A habit I have got myself to use is to keep a container (usually a sour cream or yoghurt container) with enough Windex in it to completely immerse the color cup or bottle I'm using. Once I'm done with the painting, I drop the cup into the Windex to soak while I clean the airbrush. Usually I just have to remove and rinse, though I run a pipe cleaner through the tube "just to be sure" but it's always comes out clean as a whistle.
I reuse the Windex and save it in an old container, it is a rather repellent shade of green now...
edit D'oh! You guys probably all have gravity fed ABs, I use a Badger 150 siphon. Tom (tho9900) recommends an ultrasonic jewellry cleaner. I'm surprised he didn't this time! /edit