So many of the Youtube downloader extensions redirect you to shady third-party sites with loads of ads to do the downloading. This does direct downloads from Youtube, and while it appears to integrate with FFMPEG, it doesn't require it. This is the one to get.

Only one minor niggle; would prefer to have the list of formats available in the download panel available from the popup; I use a greasemonkey script to make the video player full-screen and it doesn't play nice with the extension, so for anything but the quick download I have to disable that greasemonkey script. But it's a minor thing, I can disable the greasemonkey script when I need to.