It can be done using a javascript in google chrome.
To do this right click on the bookmarks bar in chrome browser and select 'Add page', you can name this page something as 'Download Youtube Video' and enter the javascript mentioned below in one line in the URL box:
javascript:window.location.href = 'http://youtube.com/get_video?video_id=' + swfArgs['video_id'] + "&l=" + swfArgs['l'] + "&sk=" + swfArgs['sk'] + '&fmt_map' + swfArgs['fmt_map'] + '&t=' + swfArgs['t'];
After doing this, if you go to Youtube.com and start any video and then click on 'Download Youtube Video' to start the download of that video. You can see the progress of video download at the bottom of google chrom browser window.
The downloaded video will have name as 'get_video' and won't have any extension, Rename this video file to whatever you want with .flv extension and one of the way of running these .flv video is using 'VLC Media Player' which you can download for free.
