Ok, so this one raises a plethora of copyright issues but that's something for you to deal with yourself. This is just a little trick I discovered I thought I'd share. It might be that a client can't find an original video you want to stream from Facebook (which is what happened in my case) or for whatever reason.
Go to a video. Go to the URL at the top of the page. In front of the word YouTube type 'ss' (after the www.) like www.ssyoutube.com/watch?... You'll then be redirected to the savefrom.net service and you can choose the resolution you want to save out to.
They also support other video and audio channels - Vimeo, DailyMotion, Soundcloud, blah. Yeah, it feels a bit 'grey hat' but it might be useful. It's good one if you want to knock up animated GIFs to boost click-through on Twitter, or whatever. Give it a punt.