Your ceiling in the kitchen gets a lot of smoke and heat that rises during cooking. Over long periods of time, it can cause some grime to build up on the ceiling. Take a moment to wipe down the ceiling in your kitchen.
This depends on the type of stain and the type of texture on your ceiling. The most common stains are grease grime, water spots, and pen marks on walls. If you have a textured ceiling, this makes it really difficult because cleaning these will probably remove the texture. In addition, some removal techniques for water spots require you to put a paint primer on and to repaint the area with the original paint.
Pen marks can usually come out with some cotton swaps and rubbing alcohol. Grease stains might need a product called TSP mixed in a water solution that is applied with a damp cloth to scrub the greasy film off. Then use a dry cloth to bring it all up. Water stains might require some sand paper to sand down the area, and then apply a primer and the paint.
Here is a great video from About.com about these different techniques.