Download the whole video into the Youtube window (make sure the bar goes all the way to the end).
On IE web browser select 'Tools', then 'Internet Options'.
In the window that pops up select 'Settings' in the 'Browsing History' section.
Another window will pop up - select 'View Files'.
This will open the 'Temporary Internet Files' folder. Scroll down to the bottom and look for a large file called "Get_Video?VideoID=" (will have a load of characters after it). Right click on the file name and copy it. Now paste it somewhere else in your computer (desktop/ folder/ wherever). Once you've done this you need to add the extension ".flv" to the filename, and you can also rename it.
All you need now is an FLV player, or I'm finding that Windows Media Player is happy to play them! Just drag and drop the file (or open via the menu) into the appropriate media player.
There are also some pieces of software that allow you to capture streaming video on your computer by selecting an area of the screen and then 'recording' it. I haven't found any free versions of this yet though.
Lots of options available
