A bore is someone or something that is boring. A boor is a clumsy or ill-mannered person. A boar is (1) a species of wild pig, and (2) the adult male of several species of mammals.
Bore also has several definitions relating to holes—most generally, (1) to make a hole through, and (2) a hole made by boring. It’s also the past tense of the verb bear, and it’s a noun for a tidal wave that travels up a river or narrow bay. In modern English, boor has no definitions unrelated to clumsiness or poor manners, and boar has no definitions unrelated to animals.
Examples
Even the normally reliable Fassbender is a bore as the droid with a not-so-secret agenda. [Columbia Daily Tribune]
Clementi appears to have been coming to grips with his sexual orientation and Ravi was acting out as a rather despicable boor. [New York Daily News]
Killing wild boar with bows and arrows may sound primitive, but the National Parks Board (NParks) is considering the method to curb the animal population. [Straits Times]
Charlotte is meant to be the film’s free spirit, but she’s a pedantic bore. [Boston Globe]
The media and the public reliably conflate substantive moderation with declining to behave like a complete boor. [The Christian Century]