Via John Gruber at Daring Fireball, I've learned that a company called Sarcasm, Inc., is marketing a "Sarcasm punctuation mark" called SarcMark, which people are supposed to use to "emphasize a sarcastic phrase, sentence or message". John Gruber's pitch-perfect assessment:
What a great idea. I'm sure it'll be a huge hit.
According to Wikipedia, the stock of Eastern emoticons includes one conveying "shifty, suspicious: could also be sarcasm": (< . <) And the full list of emoticons gives :-! and ¬¬. I'm not familiar with any of these free options. I think one can begin to get a sense for why there isn't really a dedicated sarcasm emoticon by looking at the "Best examples" that Sarcasm, Inc., provides. Even having been told what the SarcMark is supposed to do to an utterance, I find all those examples confusing. To the extent that I can make sense of them at all, I seem to need to ignore the SarcMark or interpret it as the trusty :-) or ;-), which convey complex, nuanced meanings that are not inherently sarcastic but which can, of course, be used sarcastically.
I didn't purchase the SarcMark, so I probably can't reproduce it here without getting in trouble, hence the free alternative in my title.
Update at about 2:30 PST: In the comments, Ben Zimmer links to his 2007 LL post Punctuation, now with heightened indifference, which has more details and a useful historical dimension.