Changed out water valve but hear the icemaker "clicking", still calling for water. Any ideas. Happened once before but changing out water valve fixed it.

You cannot fix appliances by blindly changing parts. Was the solenoid on the water valve open or was it good. What did you get on the ohm meter before you changed it? You should unplug the plug going to water valve and using a voltmeter check to see if it sends 120 volts to solenoid when it clicks and calls for water. You can pop off the end of the icemaker and try pushing in on the microswitch to see if it sends power to the plug that goes to the water valve. You can also unplug the unit and using the ohm meter test to see if the microswitches are closing when the buttons on them are pressed. If one is not closing the circuit then you will know to replace it. Are you sure that water can get through the water valve?
Look at these manuals: https://dl.dropboxusercontent.com/u/8010163/R-106%20Whirlpool%20Icemaker%20Troubleshooting%20Ser vice%20Manual.pdf
https://dl.dropboxusercontent.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf
https://dl.dropboxusercontent.com/u/8010163/Maytag%20Refrigerators.zip
You will have to use a meter to find out what the problem is that is keeping the water valve from working. Changing parts is not troubleshooting, it's guessing and does not work too often. I do not know why people do this instead of first using a $10 meter to find out what is wrong.