Probably Caffeine is mildly addictive. But there are at least two forms of addiction, physical and psychological. If you are physically addicted and stop taking a drug then you are going to experience physical symptoms. If you are psychologically addicted you are going to miss a substance you like and are used to but you shouldn't get a physical reaction.
Caffeine is a bit of both, though people argue about this. Wikipedia lists the following as caffeine withdrawal symptoms.
headaches,
muscle pain and stiffness,
lethargy,
nausea,
vomiting,
depressed mood,
marked irritability
My feeling is that you would have to consume an awful lot of caffeine over a fairly long period to generate stuff like that. Most people who are addicted to caffeine have a psychological addiction anyway. I am not at all convinced that significant physical addiction to caffeine exists. I read one paper that claimed 100 mg Caffeine per day was sufficient to induce addiction but it failed to mention how long you had to consume it for. If Caffeine is causing you sleep problems then
your idea of cutting back is sound. Just remember that Tea and Coca-Cola contain significant amounts of Caffeine. I dread to think how much Red Bull contains.
