Crowns

In other cultures no crown is used in the equivalent of coronation, but the head may still be otherwise symbolically adorned, as a royal tikka in the Hindu tradition of India.
As an emblem
A crown is often an emblem of the monarchy, a monarch's government, or items endorsed by it. The word itself is used, particularly in Commonwealth countries, as an abstract name for the monarchy itself, as distinct from the individual who inhabits it. A specific type of crown (or coronet for lower ranks of peerage) is employed in heraldry under strict rules. Indeed some monarchies never had a physical crown, just a heraldic representation, as in the constitutional kingdom of Belgium, where no coronation ever took place; the royal installation is done by a solemn oath in parliament, wearing a military uniform: the King is not acknowledged as by divine right, but assumes the only hereditary public office in the service of the law; so he in turn will swear in all members of "his" federal government.