No, there are programs that claim to be able to do this and check who is looking at your profile, they are all spyware or virus though. DO NOT use these apps/programs.
You don't say how you know they are downloading? You need to set your security so that only friends can gain access. Then cull your friends to real ones. Alternatively, you may have been hacked, in which case you can open another email account and start over with a new name. Close the other account down by deactivating. Good luck.
that was super fast guys. That kind of sucks. Had a weird incident where found loads of my facebook pics on someone's desktop. was just wondering if there was some kind of downloaded pic alert/notification. I know half the people use face book for spying and ...(you know what) but its just kind of funny when you actually see it being done to you and a bunch of other random random people. hee hee : )
If you call ALL your pictures private .. and then make them available for anyone to download .. they are then global .. worldwide property .. and what do you expect?