One of my favorite scenes in the movie Clueless is the scene where a pretentious college student quotes Shakespeare to back up some asinine point she's trying to make: "It's like Hamlet said, 'To thine own self be true.'" Cher (Alicia Silverstone), who saw the Mel Gibson version of Hamlet, points out that it was Polonius who said that, exposing the college student as a poseur who quotes works that she doesn't even remember accurately.
Anyway, "To thine own self be true" has to be the number-one "out of context" quotations -- literary quotations that are presented ironically or even unfavorably in context, but which are taken out of context and quoted as if they were supposed to be the author's pearls of wisdom. Polonius's big speech in Hamlet is one big collection of vapid cliches; "To thine own self be true," coming right at the end of the speech, is at once the biggest cliche of all and a perfect punchline (after many lines of setting out exactly how Laertes is supposed to behave, he tells him to be true to himself). To quote it as Shakespearian wisdom is to overlook the fact that Shakespeare didn't present the line as wisdom, he presented it as a joke.
Number two out-of-context quote is probably Shakespeare again: "The first thing we do, let's kill all the lawyers," which, as was pointed out on the TV version of -- yes -- Clueless, is spoken by a bad guy. (Though even in context, it's still a funny lawyer joke.) Number three is Browning's "God's in His heaven, all's right with the world," which comes off rather differently in the bizarre dramatic poem it appears in, since it's sung by an innocent mill-worker and overheard by a man in bed with a woman whose husband they just murdered (sort of Double Indemnity in Victorian verse and set in Italy).