How to copy YouTube video clips  

SOME USEFUL TIPS:
      1. If you wish to listen to a YouTube song over and over again without having to click on the Replay button each time, just copy the URL of the song (the line starting with http://www.youtube.com/....) and then paste it in the box here (click to go to the http://www.tubereplay.com website).
      2. If you want to jump to the middle of a YouTube clip, let's say at the 2-minute spot, just type (add) the following to the end of the URL &t=2m0s (t is for time, m for minutes and s for seconds). Take a look at this YouTube of a live performance by Paul McCartney in Spain: http://www.youtube.com/watch?v=1nq_-DHhVOg&feature=related. For the first 2min 30sec he was just talking to the crowd. So if you want to cut out all the talk and go straight to the song just type &t=2m30s at the end of the URL which now becomes http://www.youtube.com/watch?v=1nq_-DHhVOg&feature=related&t=2m30s. Click on it and you will see that it starts at the 2min 30sec point of the clip.
      3. How to copy a song or a speech from a YouTube video clip so you can play it in your mp3 player (see Item 3 below).
      4. Want to know which are the most-watched video clips in YouTube of the moment? Go here.

(Updated on September 3, 2017):
It is indeed very simple to download a YouTube clip to your computer for later offline viewing. Open the clip, copy its address (url) then open this site and paste the url in the "Convert a video link/url" box. Choose the format you want (.mp4 or .avi, for example) and it will convert it immediately for you. When it's done it will ask you where you want to have it copied to. That's all there is to it and you can listen to the clip at leisure indefinitely - and offline!

There are a few programs that make it possible for you to copy the video clips that you like from YouTube into your hard disk but these are two of the simplest:

1. If you only do it occasionally follow the steps below:
From the YouTube's url (eg. https://www.youtube.com/watch?v=ytvcdSzzMds for Tom Jones' Green Green Grass of Home) copy the part after the question mark (in this case v=ytvcdSzzMds and add it to this https://savemedia.com/watch? so the new url that will enable you to download the clip is now:
https://savemedia.com/watch?v=ytvcdSzzMds. Try it out.

2. If you have many YouTube or Daily Motion files to copy:
Install aTubeCatcher from here. It's completely free. But if you don't want it to automatically change your settings I'd suggest that you choose "Custom installation" instead of "Typical installation". You can then untick "Install the aTube toolbar and make Ask.com my default search provider" as well as "Set my home page to Ask.com" (these are two examples of how your internet settings can be changed without your knowledge if you let it install automatically). Once it is installed, each time you want to copy a YouTube clip that you like you only have to copy its url and paste it on the aTubeCatcher box. (To avoid problems in opening the copied file, you might want to choose the .avi extension from the number of extensions provided).

3. If you just want to copy a song or a speech from YouTube:
But what if you just want to copy a song from a YouTube video clip so you can play it in your mp3 player? You have at least two choices:
(i) Copy the url of the YouTube video clip that you want convert to .mp3 then go to the online video converter website here.
In fact if you click on the above link a page entitled "Extract a sound from a video" opens that says "Paste your url here". So just paste what you have copied there and then click on "Download" followed by "Convert". When it has finished the conversion, click on "Get" and then save it to where you want it to be.
(ii) Or you can install a software (it's completely free) that specializes in this and will save YouTube videos on your computer as .mp3 or .wav files. Again you need only to copy and paste the url. The program is called "Youtube To MP3". You can download it from here.

4. How to play the same YouTube over and over again:
From the YouTube's url (eg. https://www.youtube.com/watch?v=ytvcdSzzMds for Tom Jones' Green Green Grass of Home) copy the part after the question mark (in this case v=ytvcdSzzMds and add it to this http://listenonrepeat.com/watch/? so the new url for non-stop playing of the clip is now:
http://listenonrepeat.com/watch/?v=ytvcdSzzMds
Here, to make it easier for you, here is the site where you have just to add the v= part in the address line. Click.