WolframAlpha failing to aswer the Last Question: How may entropy be reversed?
Although, I guess we have to give it 20 bil­lion years or so before we really write it off.

Edit 20 Dec 2009: I’m not sure when, but it looks like it’s figured out the cor­rect non-​​answer (and in a good deal less than twenty bil­lion years):

WolframAlpha getting the 'right' answer to The Last Question