Are you the kind of person who dyes your hair a different color all the time? If so, I would probably go with natural, or what is on your driver's license. If you dye your hair, but constantly go with shades of brown, I would put down brown. I've had my hair light brown with blonde highlights and strawberry blonde, but my hair is naturally a dark brownish red, so I always just said my hair was brown, because even the red could look sort of a brownish color
I know for the US of A passport application (since we do not know where you are from, these answers could be wrong). On the US passport app, you list your natural hair color. They do not care that you dye it. Everyone can dye their hair. They want to know the "real" color your hair. What it says on your birth certificate which you will also be supplying to them. You send them the original birth certificate (no copies are accepted) and it is returned to you with the passport.