On YouTube, I remember after you have finished watching one video, that would be that.
No other video would play until you clicked on another video.
Now it seems whatever video I click on to watch, after it has ended, it plays another one automatically.
Is there a way to stop this happening?
Or is this a new feature and it happens to everyone whatever they want to see?
Could someone explain? Thanks.

I've noticed it for a few weeks. It plays the next video from the playlist on the right.

I'd also like to know if i could switch it off!

Top right there is a button "autoplay" which is on - by default.

There is a browser plug-in for firefox and tips for Opera & Chrome:
http://www.hongkiat.com/blog/stop-youtube-autoplay/