After you’ve downloaded and installed FxVisor, launch it and you will immediately be given the choice of removing any arrow overlay from shortcuts or replacing the overlay with a different style which isn’t as much of an eye sore.

If you have removed the arrow overlay, FxVisor will also allow you to re-enable the default overlay. All in all, FxVisor is a great little application which will be of much help to any users who use desktop shortcuts to launch their applications, though I still recommend using differents methods for application launching.

Update
Apparently this will only work on Windows Vista. For those of you using Windows XP, the TweakXP Tweaking Utility will allow you to remove the arrow overlays, supposedly.