Having a YouTube account offers you the option to save videos you like to your Favorites to view later, without having to run a search for them. If a video gets taken down by YouTube or by the user, accessing it from your Favorites will no longer be an option, but a disabled version will remain there. In this case, or if you simply don't want a saved video anymore, you can delete the video from your Favorites easily.
Navigate to youtube.com, log in to your account and click the drop-down arrow next to your username. This opens a dialog box on the page.
Click "View list" under "Favorites" in the dialog that appears.
Check the boxes next to the videos you want to remove, then click the "Remove" button. The videos you selected will be deleted from your Favorites.