As far as I know, aspirin, acetaminophen, ibuprofen aren't addictive (except maybe mentally). It's best not to take aspirin without a doctor's involvement. Ibuprofen is often prescribed (though it's OTC), for pain--even long-term for chronic pain. Again, professional advice/monitoring is recommended for more-than-occasional use.
Anything containing caffein is addictive for most peeps in the same way coffee is addictive, with the same sort of withdrawal symptoms. Headache usually, sometimes quite bad, but usually it doesn't take more than a few days. Other than that, these OTC pain meds are not addictive, certainly not for most of us.
The thing is, if you're suffering chronic pain, you should know why, if at all possible. AND (and this is marvelous to me) a heluva lot of chronic pain can be stemmed by simply moving your body on an extended and regular basis.