Download Cleaner Lite от Daniel Betz

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.