I have just stumbled across a site which will allow you to download Youtube videos directly without installation of any Video downloader or any other tool.
1) Open a video on youtube (or copy the URL if you already know it)
2) Select the beginning part of the video's URL "http://www.y" from "http://www.youtube.com/"
3) Change/ delete the selected part and just type "3"
4) The URL will now look like this "http://www.3outube.com/"
5) You will see many options of downloading the video
An easy step by step snapshot is also available on the website itself