As far as Facebook, the web site, goes -- you can't. They don't provide any way to download the videos via the Facebook website that I know of.
One alternative is to use browser extensions that allow you to download videos from, in fact, any web page:
DownloadHelper is a tool for web content extraction. Its purpose is to capture video and image files from many sites. Just surf the Web as you are used to, when DownloadHelper detects it can do something for you, the icon gets animated and a menu allows you to download files by simply clicking an item. For instance, if you go to a YouTube page, you'll be able to download the video directly on your file system. It also works with MySpace, Google videos, DailyMotion, Porkolt, iFilm, DreamHost and others.
FVD Video Downloader – a browser plugin that allows you to download video and audio files from almost any page for further viewing on your computer. It supports a huge selection of sites including Facebook, Vkontakte, Vimeo, Veoh, Blip, Metacafe, Dailymotion, Break as well as thousands of others. It is very easy to operate the plugin – if there’s a downloadable video available on the page that you are viewing, the arrow button in your browser changes its color to blue. You can download the video by clicking on this button. After that you can play it on your computer or convert it into another format for further viewing on other devices.
Note that for political reasons the FVD downloader won't work on YouTube, because the official Google Chrome add-in repository policies prevent it.
If you don't use Firefox or Chrome
First, try the Facebook Video Downloader User Script. User scripts work in most common browsers now. Click the big green "Install" button on the upper right of the userscripts.org page to set it up.
Creates a download link, link is added to the description box of the video. NOTE: You need to open the link in a new tab as it does not support theater mode.
Another alternative, if you are using Windows, is software that pulls the video files out of the browser cache like VideoCacheView.
![videocacheview screenshot](https://i.stack.imgur.com/RmhTv.png)
You can do the same thing manually if you navigate to where the browser cache files are on your OS / Browser, and sort by filesize.
People who confuse first name and Facebook username request password reset with your Facebook username (which turns out to be a first name in your country). There is no way to prevent such e-mails, apart from creating in your e-mail client a filter based on some keywords present in such password reset e-mails.
![enter image description here](https://i.stack.imgur.com/yIoan.png)
UPDATE (2014-02-05): Just saw this screen:
![enter image description here](https://i.stack.imgur.com/VChTC.png)
right after
![enter image description here](https://i.stack.imgur.com/1Z7ui.png)
which is the page you land on when clicking on "Click here to change your password." in the email. Not sure how often it appears.
Best Answer
The only information the provide on this is from Facebook Help:
Beyond this, it's impossible to say what they do to the videos uploaded to them. Chances are they will re-encode all videos regardless of what comes in, to ensure they are exactly what they need them to be.