Usually it starts leaking coolant. There is a little "weep" hole on the water pump. When it starts leaking it's usually time to replace it.
If it's making noise, this too could be an indication of a bad pump.
They aren't very complicated really. They are turned by a belt and they circulate the coolant. The problem is, when they go bad, they can cause the vehicle to overheat which may cause more problems.
The water pump generally is replaced when you do a timing belt, whether it's bad or not. Because there is no extra labor involved when they do a timing belt, it's a good idea. It can be expensive to do on it's own.
Check your owner's manual and see when your timing belt is due to be changed, this is usually when the water pump is replaced as well. Otherwise they don't usually go bad.
If you feel they are not telling you the truth, take it somewhere else for a second opinion. Good luck.
〉 Answered on Mar 23rd, 2008 by Lori Johnson, Owner and Instructor at Ladies Start Your Engines