File Download Log
Everytime a file is downloaded there's an entry made in the File Download Log.
To access it go to Downloads → Reports → Logs and choose File Downloads from the dropdown. Once there you'll see a screen similar to this:
The Downloads column lets you click a download and see only the rows for that item.
The User column lets you click a user and see only rows from that user.
The Payment ID column lets you click and ID and see information about the original transaction.