Apparently everyone knows how to download FLV videos from web addresses which use the Youtube syntax:

http://www.youtube.com/watch?v=

Using the bookmark feature:

1. Right click on the bookmarks bar of Google Chrome.
2. Type the name to what ever you want (eg. Download YouTube).
3. Use the following code as the URL:
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   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'];

   1.  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']; 
4. Go to the YouTube website and to the page of the video.
5. Click on your bookmark and Google should say it's downloading the FLV file

Using the bookmark feature and convert to MP4:

1. Right click on the bookmarks bar of Google Chrome.
2. Type the name to what ever you want (eg. Download YouTube).
3. Use the following code as the URL:
   copyrawstyler

   javascript:window.location.href = 'http://youtube.com/get_video?video_id=' + swfArgs['video_id']+ "&fmt=18" + "&l=" + swfArgs['l'] + "&sk=" + swfArgs['sk'] + '&fmt_map' + swfArgs['fmt_map'] + '&t=' + swfArgs['t'];

   1.  javascript:window.location.href = 'http://youtube.com/get_video?video_id=' + swfArgs['video_id']+ "&fmt=18" + "&l=" + swfArgs['l'] + "&sk=" + swfArgs['sk'] + '&fmt_map' + swfArgs['fmt_map'] + '&t=' + swfArgs['t']; 
4. Go to the YouTube website and to the page of the video.
5. Click on your bookmark and Google should say it's downloading the MP4 file

Software-wise personally I use:

• Moyea YouTube FLV Downloader
• Free Download Manager
• DVD VideoSoft - Free YouTube to Mp3 Converter

all of which are free to download and use.