> This sentence is false.

The famous [liar paradox][1].

As the wiki article explains:

> If "this sentence is false" is true,
> then the sentence is false, which
> would in turn mean that it is actually
> true, but this would mean that it is
> false, and so on ad infinitum.
> 
> Similarly, if "this sentence is false"
> is false, then the sentence is true,
> which would in turn mean that it is
> actually false, but this would mean
> that it is true, and so on ad
> infinitum.

  [1]: http://en.wikipedia.org/wiki/Liar_paradox