How to Embedd youtube video in body field (converts URLs into embedded players)?
I’ve found and tested this module which do excaly what I want :

Url to Video Filter


  This module adds a new input filter that automatically converts URLs
  for various video sharing websites into embedded players into the
  text.


Here is a screenshot of the CKEditor filter :



I’ve tested this module on multiple sites and it works very well. 

Currently this module supports the following services : YouTube / Vimeo

EDIT
Now, It also supports Youtube URL with parameter like ?rel=0 (rel=0 is used to disable related videos shown at the end of a video)