For 12.04:
The relevant file is now at:
/usr/share/unity/5/panel-shadow.png
You can delete it, you can rename it, or you can back up the original image and used Gimp's eraser to make the image transparent (just erase the whole thing).
If Unity can't find it, it won' t complain (or show it to you).
Keep in mind that whenever Unity is updated, it will replace the shadow image file, and you'll have to repeat your fix accordingly. If you find yourself forgetting what file it is you modified (or where it lives) you can try renaming it to something more memorable, like annoying-panel-shadow.png
. Then you can just type $ locate annoying
and quickly find the right folder and file to update.