U.S. Secretary of State Hillary Clinton has declared.....

1 and 3 are both correct.

1 is correct because without the "The", you are giving the title and name of a person together. A comma is not required.

2 is incorrect because when you add the "The", you are no longer putting the name and title together. The sentence would be correct if you just said, "The Secretary of State just declared...."

3 is correct because if you add the the "The", the title and name are no longer a unit so you now have to name the person and put it after the comma.