I think most constitutions have an equivalent. What is unusual about the US is the extent to which there is judge made legislation through re-interpretation and extension of those rights. THis is not just true in the west. Here is the Sri Lankan constitution: https://www.parliament.lk/files/pdf/constitution.pdf - take a look at Chapter III. It is common for cases to be brought under these provisions.

There are international treaties that are incorporated law - e.g. the European Convention on Human Rights. How effective they are varies with national governments (Russia and Turkey are both ECHR, for example). The big variable is whether a country has an independent judiciary that will enforce those rights.

There are definite rights listed in very old laws such as the Magna Carta - and I have read that much of what it granted was already accepted in common law.