If you won't be downloading videos often and you want to use what is (most likely) already on your pc or you just enjoy taking the scenic long way round, VLC + your browser. This method is less elegant than a dedicated application but hey, it works! Note, in my experience this will always download videos in the highest available resolution upto 720p.
1. Copy the complete youtube URL of the video you wish to download.
2. Open VLC and open the 'File/Open Network' menu. A dialogue box will open.
3. Paste the video URL and press 'Open'. VLC will start to play the video in a few moments.
4. Find 'Media Information' from the menu. For the my version of VLC its under 'Window' but this will vary depending on your OS. A dialogue box will open
5. Copy the URL in the box labelled 'Location' and
6. paste it into the address bar of a new tab in your browser and open it. This URL will also work in download managers that don’t normally have a Youtube function. (you can close or stop VLC at this point to save bandwidth)
7. Depending on your browser, the download will either begin immediately and you are done or the video will begin to load in a player, in which case
8. open your browser's 'File/Save' menu. At this point you can name the video. If your browser does not automatically fill in the file extension, just use '.mp4'
9. Once you press save, the video will begin to download. You can then close the tab and let the video download in the background.
*See the colourful illustrated guide here! http://i.imgur.com/QMDoLDs.jpg