Figuratively.

Thanks for clarifying. Sorry for this long reply but it is a tricky thing to make clear because of the nature of both of these words. My point is that "literally" is not actually used to be synonymous with "figuratively" in most of the cases where somebody might police it. Instead, I'm just saying that the figurative usage of "literally" is distinct from using "literally" to literally mean "figuratively", and also that that (totally fine) figurative usage seems to be the most commonly complained about. Though the dictionaries often conflate the two, as far as I can tell real usage is more subtle than "these are synonyms", and also is consistent with the primary meanings of both words. OK that's a lot of these words. An example!

If I say "That comedian literally brought the house down last night," you might correct me by saying "Don't you mean he figuratively brought the house down?", and I think that's a misunderstanding. A metaphor like "brought the house down" only functions because you are saying something that contradicts reality in the first place. So I didn't misspeak when I said "literally" - I would never have intended to say the sentence "He figuratively brought the house down" because that much is clear from context... Pointing out that a metaphor was figurative would actually weaken the metaphor. What I was intending to do was be more emphatic about the trueness of the metaphorical statement, so that the metaphor would be more vivid. This is a dumb example of that but that's the function the word has when it is within a metaphor, and not describing the metaphor.

People often want to heighten things to express meaning beyond the usual level of a phrase. I could say "He really brought the house down" or "He actually brought the house down" and I would probably not be corrected as much, even though both of those words are synonyms of "literally". I might even get away with saying "He truly brought the house down".

Of all those options, I think "literally" sounds the most emphatic, precisely because of its meaning of "take this in a literal sense." It intensifies the basic conceit of a what a metaphor is: a blatantly false statement intended to provide some other meaning. People are not trying (and failing) to tell you the nature of the metaphor, they are trying to increase the strength of the metaphor. "Literally" is also attractive because it sounds funny, and maybe once it got a bit trendy for a while it got in people's heads as a common word to reach for when emphasis is needed.

Of course, there can be "wrong" uses of both words, but the mere act of using "literally" in a figurative context is not one.

You have been polite and made a clear case, but many of the people who roll their eyes in condescension when they hear this "mistake" are not. They act like the speaker is an idiot who has, ironically, used the word that means the opposite of what they think they mean. This happens with a few other language issues - people know a simplified version of a "rule" and then correct others' usage based on this, without understanding that the rules we learn as kids are nothing more than guidelines to help us do pretty much the right thing without getting into the complicated reality of language.

I think policing makes sense in more confusing cases, or in legal situations (e.g. "I had to hit him officer, he was literally asking for it."). Or where somebody clearly just misunderstands what they are saying and confuses both words. But I don't really see sentences like "Shakespeare used language literally in his poems, in order to express the beauty of his beloved." in the wild, do you?

aand right at the end I found a much better expression of this idea here: http://blog.dictionary.com/literally/