Problem
WordPress allows you to attach downloads to pages (e.g. the Ashford theme WinZip file). It does not keep track of the number of downloads. While you can use Google Analytics to track your downloads, you can not reveal that number to your visitors.
Solution
This plugin allows you to track your downloads and display statistics.
Use case
One of the principals of persuasion is to provide social proof that your product or service is used successfully by other people. A download counter can be used to reinforce that principal.