There's quite a few youtube plugins for Firefox.
Install Firefox:
sudo apt-get install firefox
Fire up Firefox .. then go to
Tools>Addons>Extensions .. in the search box enter
easy youtube video downloader and hit enter.
Click the
Install button next to "Easy Youtube Video Downloader 6.6".
When installed .. restart Firefox.
Now when you visit any Youtube page .. there will be a "
Download" button under the video where you can choose the download format
I suggest you download them as .flv or they might get quite large

.. but if it's music, you can download them as .mp3 (ie. without the video) if you wish.
There's a few for Chrome/Chromium too .. but I've not tested them:
http://www.chromeextensions.org/?s=youtube&scat=allThis seems to work in Chromium (just tested it):
http://www.chromeextensions.org/utilities/ultimate-youtube-downloader/for video it just works .. for mp3 conversion it takes you to an external site, where you click the download link