O.K the question you have asked is a common one.
Here is a software which is free on download and allows you to save your downloaded video in FLV format:http://funadvice.com/r/154bcetatv0
Here is a site which allows you to download your favorite Youtube videos:http://funadvice.com/r/3mqngbji2l
Here's the Brothersoft link to download Youtube player: http://funadvice.com/r/3mqnkm49ld
I hope my comment was of help.
firefox has a video download helper add-on or you can det realplayer and it has an option to do that.
use http://funadvice.com/r/3mqngbji2l :)
your welcome :)