The general public tends to be pretty cavalier about pain meds--and self-medication overdoses are what cause the problems. Both NSAIDs and acetaminophen can be used safely when on warfarin, but only under doctors' supervision and absent mitigating circumstances (like gastric problems or GERD with NSAIDs, liver problems with acetaminophen). Using recommended doses, only when needed, and letting the docs know what you're doing is always the wisest course.
Since I have to load up on statins and other meds that affect my liver, I stay away from acetaminophen as a general rule (although I did take some arthritis-strength Tylenol when I was weaning myself off narcs after surgery). I had to rely pretty heavily on ibuprofen after that, but it messes with INRs, so I've weaned myself off of pain meds in general, except when I'm getting a migraine or something (when Tylenol wouldn't do squat anyway).
If you don't absolutely have to take a pain med, don't. Listen to music, put a hot or cool cloth on your head, get a massage, have a nice cuppa--etc. Most of the time we just reach for the stuff without thinking. And the idiots of the world OD on the stuff and then everybody freaks out.