How to play (repeat) you tube videos in a loop?

If you are embedding you tube player in a website, there are lots of way to do this, here i am going to explain using iframe  version. So if you are using iframe version for embedding, you can do like this:

 <iframe width="560" height="315" src="http://www.youtube.com/embed/Your_Video_Id" frameborder="0" allowfullscreen></iframe>  

The <iframe> tag below would load a 560x315px player that would play the YouTube video. Since the URL sets the autoplay parameter to 1, the video would play automatically once the player has loaded.

 <iframe width="560" height="315" src="http://www.youtube.com/embed/Your_Video_Id?autoplay=1" frameborder="0" allowfullscreen></iframe>  

If you want to loop YouTube video, set the loop parameter value to 1 and set the playlist parameter value to the same video ID in the embed URL, Here is the example of iframe version:

 <iframe src="http://www.youtube.com/embed/Your_Video_Id?autoplay=1&loop=1&playlist=VIDEO_ID" width="560" height="315" frameborder="0" allowfullscreen></iframe>  

References:
https://developers.google.com/youtube/player_parameters#Manual_IFrame_Embeds
https://developers.google.com/youtube/player_parameters#loop