Browser extensions to help users to download online videos hosted on video sites like YouTube and Vimeo. …
Easy YouTube Video Downloader
For Firefox. Open source. As the name suggests, supports only YouTube.
Video DownloadHelper, aka DownloadHelper
For Firefox. Proprietary. Many supported sites. Optionally can convert downloaded files into popular formats. Using Windows, the conversion adds a watermark which can be removed with a paid upgrade. On Linux, there is no watermark. Complicated to set up (especially on Windows) and configure, and users I've set it up for find it complicated to use.