If you use Firefox or Chrome, you should know that they keep a history of everything you have downloaded. You can clear it easily but its better to disable it if there are multiple users using the same computer. There is no doubt you can clear your download history from the download manager, but there are times when you forget to clear it which can put your privacy at risk. If you don’t want anyone to find out what you have downloaded, and are concerned about your privacy, you can disable Download Manager in few simple steps.
Go to Firefox options by clicking on Firefox Menu > Options > Options.
Go to Privacy tab and under History section, select Use Custom Settings for History from the drop down menu.
Uncheck Remember Download History and click OK.
Now, Firefox will not save the files or anything you download using Firefox.
Of course, if you’d only like the list to only be cleared once you exit Firefox you can adjust that from the config.