Unknown USB Device

After my many re-installations of Windows 7, I often have an “Unknown Device” in the list of USB devices shown by the Windows Device Manager. It is almost always because of my LogiTech G110 keyboard. It works as a USB keyboard with no additional setup after these re-installations, but its extra functionality (like the cool lighted key caps) require that the device driver be installed. Doing so invariably removes the last “Unknown Device” warning from the device list.