I use ChrisPC Free VideoTube Downloader. Free. When running it, you just copy the URL from the usual YouTube dropdown and it is automatically entered in the software with a sound (if your sound is on). After several sites have been entered in the list, simply tell ChrisPC to download it to a folder you specify. Very convenient.
If the video is big or is HD, you are asked to pay ~£19 for an add-on. In that case, I use:
http://www.computerhope.com/issues/ch001002.htm
You have to click through several browser pages but soon you see a field in which to paste the YouTube address. You can specify where it will be saved.
It is one of several sites that uses only a web page to complete a download. No need to download any software. I found it by searching:
"How to save YouTube videos your computer".