In Microsoft's own words, it is impossible to install Windows XP on anything other than a hard drive. This is simply not true. By modifying a few files located on the Windows XP install disc you can!
Before you begin you need a few things: THIS FILE, an iso image of Windows XP Pro (works with SP3 and should work with SP2, other versions i'm not so sure), an iso editor such as WinISO/MagicISO/etc., and a USB stick formatted to fat/fat32 with enough space (maybe 2 gigabytes).
Step 1 - Using WinISO or another iso editor, open your Windows XP image (SP3 preferably) and navigate to the I386 folder.
Step 2 - Delete the following files:
Step 3 - Add the following files from the above zip back in to the same directory:
Step 4 - Save the iso, close the program and burn the iso to a cd.
Step 5 - Disconnect all internal hard drives, plug in a fat/fat32 formatted USB stick, power on the system, put the cd in and install to it. The USB stick should be visible now.
That's it. Plug your internal drives back in and in your computers bios set the first boot device to USB. Now whenever you plug in the stick before turning on your computer you'll boot into XP instead. Remember the USB interface is slow so the install will take some time. Even when you're done, booting into XP will be slow as well. If you use the stick on another computer, you may get a blue screen so booting into safe mode (press f8 at boot) would be advisable.