Actually they do. They study the tendencies of their opponents and then when that batter steps up to the plate, the catcher gives the sign to the pitcher for what he thinks should be thrown. If the pitcher has a difference of opinion he shakes him off until he gets a signal he likes.
A good example of this was a couple years ago when Curt Schilling was one out from a no-hitter. The batter was Shannon Stewart and Varitek, the catcher, knew that Stewart is a first pitch fastball hitter so he gave the sign to Schilling to throw a curve. Schilling thought that he would take the first pitch so he shook off the sign. Varitek again signaled for the curveball but Schilling again shook him off. Varitek then gave him the sign for the fastball, but Schilling missed his location and Stewart singled that pitch. Buh-bye no-hitter.
Schilling said afterward that he should have listened to Varitek.