You can change the icons that used to show up by default on the desktop by doing the following:

Right-click desktop > Properties > Desktop tab > Customize Desktop button > select the icon > click the Change icon button to navigate to, and select a new icon (".ico" file) > click Apply.

This works for the icons in that list.

You can also right-click an icon > select properties > look for a "Change icon" button under the shortcut tab, or look for a Customize tab to change the icon.

This is the extent of the built in abilities in Windows XP, so if you want to change icons such as drives, and others that do not have the change option in properties - you will need to use one of the alternatives mentioned by Bichur and WrecklessEric.