If you use Safari, and want to download videos then the easiest way to download youtube videos using Safari is to do the following steps:

How to Download Youtube videos in Safari

1. Go to the youtube video of your choice on youtube.com
2. Click on ‘Window’ in the menu, and select ‘Activity’
3. Under the youtube address, which will be recognisable by its name, double click on the address with the largest file listed (it should be the only one in the megabytes, but the size varies depending on length of video)
4. A new window should open and, after a few seconds, the video should begin to download to your computer

Note: You may need to use a program to convert the file into a watchable movie file.  My computer used to not recognise the file at all until converted, but for some reason it’s recently started downloading them as flash video files(.flv).