I have a WPF application which runs fine on Windows 7 OS. But the same app crashes on a particular few Windows XP machines.
It runs fine on few windows XP machine.
If I remember correctly Windows XP does not support icons larger than 48x48 pixels and this could be the reason for the crash. .ico files should definitely run on both systems.
You can create an icon that support multiple sizes, so if you add 48x48 and for example 256x256 in the same file you should be good. Also be sure to use select a good software to produce the icon when making icons that support multiple sized. I've used Greenfish Icon Editor which I think works fine. But there are multitudes of other products for this.
Be sure to read The ICON handbook, section Windows, it contains good info about what icon sizes and bit depths to use.
Other threads on SO supports my belief:
problems with icon image
Which icon sizes should my Windows application's icon include?