You can use a Firefox extension like DownloadHelper to download YouTube videos (or videos from many other Flash video sites), or any such suitable software. You can then play them with VLC. (VLC supports all the formats it could possibly download them in.)
However, for many YouTube videos, you don't need Flash at all. Enable the HTML5 beta and you will be able to view many YouTube videos using the built-in HTML5 <video> technology built in to recent versions of Chrome, Firefox, and Safari. Note that some videos, like ones with ads, don't work with the HTML5 player so you'll still need to do the above or use the Flash plugin to play them.