Technically, if you watch from you computer a video that was not on your
computer, then you necessarily downloaded it.
I personally use ViewTube:
Add GreaseMonkey to the Web browser through
https://addons.mozilla.org/firefox/downloads/latest/748/addon-748-latest.xpi/
Download the ViewTube (and, if you wish, the ViewTube+) script from
http://isebaro.com/viewtube/
Enjoy.
I use Unplug for sites that neither ViewTube nor ViewTube+ supports:
https://addons.mozilla.org/en-US/firefox/downloads/latest/2254/addon-2254-latest.xpi
Both ViewTube and Unplug allow to save the video in two clicks. See
https://trisquel.info/en/wiki/play-videos-without-using-flash for these
solutions and more.
