We hear this question a lot, and I can't help but think that there must be more to the problem than meets the eye.
Typically to keep your desktop icons how and where you want them only requires that you right click the desktop, and from the context menu choose View->remove the check from Auto arrange icons and depending on the arrangement of your icons and how the may appear to move, even so slightly you may want to uncheck the Align Icons to grid option also, that setting shouldn't completely rearrange your icons but may move them slightly to what windows considers the closest grid location.
Have you been able to test the same issue with another or newly created user just to see if there maybe some corruption with your profile (ntuser.dat / HKEY_Current_User) which keeps track of user preferences like the placement of desktop icons? If other users or a newly created user do not seem to have the same problem then you may need to consider creating a new profile for yourself and moving everything over (except ntuser.dat, ntuser.dat.log(s) and ntuser.ini). The following article may help How to Fix Corrupted User Profile in Windows 7
Hope this helps and welcome to the forums.