Just because I read yesterday an article about one paradoxe, I would like to list some today. Please notice that this list doesn't need to be complete.
A : All beliefs are of equal validity and cannot be denied. B : If that's the case, then C is correct in his belief, even though C believes something that is considered to be wrong by most people, such as that the Earth is flat. A : True. B : Then some beliefs can be denied.
Liar paradox (which is also part of the discordianism):
The following sentence is true. The preceding sentence is false.
Epimenides was a Cretan who made one immortal statement: "All Cretans are liars."
"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.
Is 'heterological' a heterological word? If the answer is 'yes', 'heterological' is autological (leading to a contradiction). If the answer is 'no', 'heterological' is heterological (again leading to a contradiction).
If everything in this box is true, then Santa Claus exists.
However a very big list of paradoxes exists in the Wikipedia of course. Have a look at it and enjoy them.