To download youtube videos and in addition, to bring in several other cool features, just follow these two steps :
1) Download "Tampermonkey" userscript and install.It takes less than a minute.
2) In google,search "Youtube Center Extension for " followed by the name of the browser you are using.I'm using chrome so I need to type in "Youtube Center Extension for chrome" and click the first link that appears and install the extension.
Now go to youtube and on the top right corner, you will see a gear icon.Click it and you may bring in many cool features as you wish.Plenty of options, including the ones that youtube's current version has omitted, have been included in it.Even without clicking the gear icon, you will be able to see the option "download" just below the videos and you can click it and select which format you need it to be downloaded in and hurray! you can download it as easily as that from nowon! :)