Quite a popular one is the Grandfather Paradox. A guy travels back in time to kill his grandfather. If he successfully kills his grandfather, then his father would not have been born, and, consequently, the guy himself wouldn't have been born, therefore, he wouldn't have been able to travel back in time to kill his grandfather, which will then result to his father being born, and him being born and being able to travel back in time, and the cycle of time paradoxes will continue.

My favorite one would be the Paradox of the Crocodile's challenge.

A crocodile stole a child from his father and promised to return the child ONLY IF the father correctly predicts what the crocodile will do. If the father predicts that the crocodile will KEEP the child, the result will be a paradox. If the crocodile keeps the child, then the father is correct and he will have to return the child to the father. However, returning the child to the father will then mean that the father guessed incorrectly, and the crocodile will have to keep the child. But then again, keeping the child will prove that the father have guessed correctly, and so on..

One favorite? impossible! Here are a few: Epimenides paradox: Epimenides was a Cretan who stated, "All Cretans are liars." Since Epimenides is a Cretan he must be a liar but if all Cretans are liars than he can not tell the truth. . The agnostic paradox. The agnostic holds that ultimate truths are unknowable. This is an ultimate truth so an agnostic can not even believe in agnosticism. Winning the game of life is a paradox because as long as you keep score you can never win.

My favourite is the 'Catch 22' paradox. This is where you may need something, but you can only have it if you don't need it.

The Catch 22 of loans and banks that gets me. I wanted a loan, for some reason or other, and the reply from the bank was 'If you had the money in your savings account, we would be only too pleased to lend you the money'

My reply to this was, 'If I had the money, I wouldn't need the loan'

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.

the thing with the bank is that they want to know that you can save that kind of money so that they know they can get it back from you but I do agree it is pretty stupid