You've not mentioned which sites you want to save downloads from. AVD is one of the few which can grab video content from multiples sites.
However if it's only Youtube that you want to rip content from, Easy Youtube Video Downloader Express is the Firefox add-on that you need:
https://addons.mozilla.org/en-GB/firefox/addon/easy-youtube-video-download/
It simply adds a nice big green 'Download As' button to your Youtube pages, as illustrated here:
http://upl.co/uploads/1647126YT11518290745.jpg
When you click on it you're given the various options available for that particular video, as shown here:
http://upl.co/uploads/1973769YT21518290821.jpg
Note though that the 'HD' and 'MP3' options won't work unless the add-on
thinks that you've made a small donation to the developer's coffee fund. (It can be any amount of your choosing). If you'd rather not do that though, simply click here to dump the relevant cookie onto your computer:
https://videodroid.org/thanks_for_support.html
The add-on will then think that you've made a payment. (Bookmark that page if you're in the habit of clearing cookies from your computer, so that you can get the relevant cookie back later)
It's also worth remembering that you can play, and save, online videos (from a wide variety of sources) with VLC. Instructions available upon request!