Enter DownloadHelper, a Firefox extension that not only supports downloading videos from YouTube, but also Dailymotion, MySpace, Google Video, and about 100 other popular and niche video sharing sites.
To download (or in this case, leech) multiple YouTube videos with one click, first highlight a region of the webpage that contains links to YouTube videos and then right-click to bring up the context menu.

One big advantage of using a browser-based downloading tool rather than a web-based one is that you have a lot more privacy. Web tools can log what videos you download, but many browser tools can work without accessing third-party servers.