I just thought I would submit this update since it seems some were posted in 2007. Mine is a GE side by side, model GSH25JSRFSS. According to GE it is 3 years old , but we moved into a new home just over 2 years ago.
Ours started this howling about a week ago, which has been best descibed as someone blowing over a glass bottle. I "Googled" GE refrigerator howling noise, and there are several links, including this forum. Dan O's answer seems to be the opinion of the majority of other posts too. The control board.
I called GE today and was told maybe it's not full enough, maybe the damper, maybe something.....then I mentioned the internet
. I was transferred to Customer Relations and they will send out a Tech. I asked why should I pay a tech if I can replace the board myself, as others have done. He said the tech would have to confirm the problem. $84.00 for the service call, but if it is the "main board" I will not be charged. I'll let you know.