No, there is no addiction to either acetaminophen or ibuprofen. No clear pharmacologic tolerance, no withdrawl syndrome (a "rebound" when someone stops a drug is NOT a withdrawl syndrome. You can have rebound with BP meds, for example, but they are not abused). Stories about addiction to these drugs are anecdotal and mythical. That one might use a medicine compulsively does not constitute an addiction.
"Where's the REST of me?"
Ronald Reagan, in "Kings Row"