Youtube users can clear the viewed videos history using the options available as part of the Youtube settings.
Step 1: Login to Youtube account (Google) and click on the username to access the Youtube menus.
Step 2: Click the Video Manager link available under YouTube.
Step 3: Navigate to the History section.
Step 4: Click the Clear all viewing history button to clear all the videos that have been watched.
Youtube also provides option Pause viewing history so that it does not keep track of the videos temporarily. If you do not want to clear all the videos from the history then you choose and remove only the selected videos.