Trash log in Mac OS X?
No - there is no general way to recover the original location of arbitrary files when you move them out of trash and place them on the desktop.

Gladly, they didn't get erased, but this is exactly the job for which Time Machine was created. Now, you can leverage some knowledge about what goes into All My Files to get things back in a reasonable shape:


Put obvious files in the correct location - Pictures, Documents, Movies, Music all have folders in the user home folder.
Create a new smart folder to search the files for "Where from" to contain http to locate any files downloaded from the internet (and perhaps placing them back in Downloads folder)


Also, since OS X doesn't really care where most user folders or applications are stored, you don't even need to do anything but file these away in a "clean later" folder and apps that need a file will automatically locate the files in their new spot.