Some Paradoxes...

Barber paradox: A barber (who is a man) shaves all and only those men who do not shave themselves. Does he shave himself?

Berry paradox: The phrase "the first number not nameable in under ten words" appears to name it in nine words.

Crocodile dilemma: If a crocodile steals a child and promises its return, if the father can correctly guess exactly what the crocodile will do, how should the crocodile respond in the case that the father correctly guesses that the child will not be returned?

Paradox of the Court: A law student agrees to pay his teacher after winning his first case. The teacher then sues the student (who has not yet won a case) for payment.

Curry's paradox: "If this sentence is true, then Santa Claus exists."

Epimenides paradox: A Cretan says: "All Cretans are liars". 

Exception paradox: "If there is an exception to every rule, then every rule must have at least one exception; the exception to this one being that it has no exception." "There's always an exception to the rule, except to the exception of the rule—which is, in of itself, an accepted exception of the rule." "In a world with no rules, there should be at least one rule - a rule against rules."

Liar paradox: "This sentence is false." This is the canonical self-referential paradox. Also "Is the answer to this question no?", "I'm lying", And "Everything I say is a lie."

Card paradox: "The next statement is true. The previous statement is false." A variant of the liar paradox that does not use self-reference.

The Pinocchio paradox: What would happen if Pinocchio said "My nose will be growing"?. Pinocchio's nose grows if he s lying.

Yablo's paradox: An ordered infinite sequence of sentences, each of which says that all following sentences are false. 

Opposite Day: "It is opposite day today." Therefore it is not opposite day, but if you say it is a normal day it would be considered a normal day.

Socratic paradox: "I know that I know nothing at all."