Credits to Jackie Moon
Info:
This Tutorial will show you how to download a program named Real Player, with the latest version of Real Player installed it allows you to download videos you watch online.
Download Video & Media Player for Free | RealPlayer
Download and Install it all.
Once all thats done go watch a video and this little icon should pop up when you mouse over.
Press it, and a window will pop up with the download.
Once the download is complete you will notice it saves the file as a FLV format.
This is what Jackie Moon didn't cover. If you want it to convert the file into a MPEG for example, you can use this program for free:
Free Video Converter - Any Video Converter Free Version - convert video to any formats, avi to MPEG, avi to MP4, flv to MPG
Download and install.
Open the downloaded video and choose a format on the right hand side of the program (it will have a drop down list) Default is Mobile format.
Click convert, once it has converted right click the folder and choose "Go to Destination Folder" not Location that will go back to the FLV
All done! Enjoi :P
WORKS FOR MORE THAN JUST YOUTUBE!