Q: What gets wetter the more it dries? 
A: A towel!

Explanation: A towel is used to dry something like a plate or your hands.  As the towel  dries your hands the towel, which was dry, becomes wet.  It is not the towel that is becoming dry, it is your hands that are becoming dry.  This joke is funny because it plays on the opposites of wet and dry.  How could something get wet as it dries?