if at a certain hour in the morning I still haven't had one, then I begin to have a headache

This is a result of a mild addiction to caffiene -- your headache is a withdrawal symptom. If you could live with the headaches for a few days (2-4, in my experiences), you would probably stop having them.

Not to say that addiction is a problem, unless it starts negatively impacting your life. If you were drinking so much caffeine that you developed heart trouble, but couldn't stop because of the horrible headaches, that might be the line where caffeine addiciton becomes harmful.

As for me, I've gone off of caffeine a number of times, and I did feel better -- didn't sweat as much, found myself able to do moderate work for much longer periods of time, and certainly stayed more hydrated (if you drink your caffeine source, you don't drink as much water, but caffeine makes you lose water faster). On the other hand, I found it harder to deal with certain kinds of stress, and had difficulty focusing (like a milder form of A.D.D.).

Plus, decaf coffee tastes like butt. ;-)