Minimize the importance of, as in That nasty review didn't bother him at all; he just shrugged it off. [Early 1900s]
Get rid of, as in She managed to shrug off her drowsiness and keep driving. [Mid-1900s]
Wriggle out of a garment, as in He shrugged off his coat. [First half of 1900s]
Dictionary.com presents 366 FAQs, incorporating some of the frequently asked questions from the past with newer queries.