Consider this trade-off the next time you have a headache: Would you take a medicine that didn’t just ease the pain but muffled your happiness too?

A recent study suggests that acetaminophen—found in Tylenol, Excedrin and a host of other medications—is an all-purpose damper, stifling a range of strong feelings. Throbbing pain, the sting of rejection, paralyzing indecision—along with euphoria and delight—all appear to be taken down a notch by the drug.

For...