Addiction means physical or psychological dependence on a medicine. Addiction can be a concern for many people who take pain medicine, especially opiates such as morphine, Demerol (chemical name: meperidine), and OxyContin (chemical name: oxycodone). According to medical dictionaries, the formal definition of addiction is compulsively using a substance even though the consequences are very bad.
Being afraid of becoming physically or psychologically dependent on a medication may keep people from taking medicine to manage their pain. If you don't have a history of substance abuse, you probably don't have to worry about addiction. The risk of true addiction is low. Talk to your doctor if you're concerned about becoming addicted to your medication. You might be able to take another medicine.
If you find that the main reason you're taking a pain medicine is for more than pain relief -- for relaxation or to relieve anxiety -- then you should talk to your doctor. Together you can decide if you should continue with that medicine or switch to another.