This sentence is false.
The famous liar paradox. 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.
Alternately,
All Cretans are liars.
or as pointed out in the comment below the Barber paradox:
The barber shaves only those men in town who do not shave themselves. Who shaves the barber?
