Download Cleaner Lite v2.3
Firefox records all downloads in your regular browsing history. This extension watches your downloads and removes them from the browsing history once they are finished and a user-configurable time has passed. This way, you can still enjoy customized address bar suggestions while not having your downloads recorded.
Important: Due to a limitation with the downloads API for add-ons (see Bug 1255507), old downloads are invisible to Download Cleaner Lite. Only downloads that happen while the add-on is installed and enabled can be acted upon. Old downloads can be removed manually from Library → Downloads.