A screen protector or not for the retina screen? Recently, I bought my very first MacBook Pro with Retina Display.

I am hesitating between having a screen protector or not.
Some claim that a protector can prevent the retina display from scratch, while others say that one can only get the best out of the retina display without any extra protection.

Is such a protector worthwhile?

Will the screen get scratched when I use a cloth to clean it, if I do not have the protector?
The points raised are both correct. While having the protector will prevent scratches on the screen, it will also reduce the quality of the display quite significantly. When I bought my Mac, I was also met with this dilemma. After having tried the best screen protector that the Apple Store had, I decided not to go with one. The display doesn't really scratch all that much, and I have not been able to induce a scratch even after using a cheap cloth. 
I would suggest you to use a screen cleaning liquid every time you use a cloth, as that is how I have been able to prevent the scratches.