For example in probability the St. Petersburg paradox. http://en.wikipedia.org/wiki/St._Petersburg_paradox

There are generally 3 resolutions of a paradox 1) The premise(s) are wrong. 2) The logic is in correct. 3) The "answer" is not self contradictory.

If the resolution is 3 then there is no contradiction. Even if its 2, there isn't technically one (just a mistake). If its 1, there might be a contradiction.

I remember discussing this with someone and coming to the conclusion that the word "paradox" really should be "paradox for me" because its only a paradox to someone until they see how to resolve it.