Astaroth

There are no universal rules, not only do different countries have different rules but different ports have different technology even within a single country and so may well have different procedures.

I wear a dress watch and silver ring, the former I take off and the later stays on and never had an issue. The Mrs does similar but has much more jewelry (silver, gold and platinum). She's had to go through body scanners a couple of times and never been asked to remove anything (and in fact cannot remove her wedding band even if she wanted to)