1. Using Java Script – Open the YouTube video page, Paste the corresponding JavaScript to the address bar and press enter.
javascript:window.location.href = 'http://youtube.com/get_video?video_id=' + yt.getConfig('SWF_ARGS')['video_id'] + "&l=" + yt.getConfig('SWF_ARGS')['l'] + "&sk=" + yt.getConfig('SWF_ARGS')['sk'] + '&t=' + yt.getConfig('SWF_ARGS')['t'];
javascript:window.location.href = 'http://youtube.com/get_video?video_id=' + yt.getConfig('SWF_ARGS')['video_id'] + "&fmt=18&l=" + yt.getConfig('SWF_ARGS')['l'] + "&sk=" + yt.getConfig('SWF_ARGS')['sk'] + '&t=' + yt.getConfig('SWF_ARGS')['t'];
javascript:window.location.href = 'http://youtube.com/get_video?video_id=' + yt.getConfig('SWF_ARGS')['video_id'] + "&fmt=22&l=" + yt.getConfig('SWF_ARGS')['l'] + "&sk=" + yt.getConfig('SWF_ARGS')['sk'] + '&t=' + yt.getConfig('SWF_ARGS')['t'];
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2. Using the youtubian bookmarklet
This bookmarklet will allow you to easily Download youtube videos (as flash or mpg). It works in Firefox, Chrome,Safari and Opera
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3. User JavaScript in Opera
getVideo.js adds a small line at the bottom of your YouTube videos that allows you to download them in multiple formats
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4. C# open source web application
I have written a web application which will allow you to download YouTube videos. Read this post. You may need to make some changes, and dont forget to read the comments on the post.