Mikey Borup provides a quick tip showing the kinds of things that are possible by using the Parent expression in After Effects. By linking to different attributes of a parent layer through expressions, you can get some complex setups for animation.

Similar, Lee Daniels recently showed how you can use simple expressions in After Effects to remove the inherited rotation from a parented object, while keeping the parenting in place. His example was a Bike Pedal Setup. Easily Create a Bike Pedal Effect in Ae by Using a Simple Expression.