worry vs worry about

You need to say "about."

Yes you should say 'worry about' otherwise it can imply you are causing someone or something else to worry, for example a dog worrying a sheep.

Both forms are used.

(Cross-posted. I do not agree with the previous replies. For me, "Don't worry what others think" seems a normal thing for someone to say. Perhaps there are regional variations.)

I would never say that (British English). Of course I would understand it.

AnonymousDon't worry what others think.

This form is syntactically defective (direct object on the intransitive use of "worry"), but it's so commonly used that it is widely accepted, even if much less than the correct version.