Curtseys and bowing is expected to someone who is higher up the royal pecking order. It is not necessary to do so to someone of the same rank.
Commoners curtsey to everybody with a royal title
Princesses and princess, irrespective of whether they are born or married into royalty or whether they are heirs or spares or neither do not curtsey to one another, but only to kings, queens and emporers and empresses or their souvereign.
All heads of state irregardless of whether they are kings, queens, emporers or in case of a principality "only" dukes or princes do not curtsey or bow to each other. Other elected heads of states and their spouses are also equal and are not required to show deference in this way either (not that they would like to anyway, being the leaders of republican countries)
I think this is country specific. In UK, no one except royals must bow. Commoners do it because they want to or think they are supposed to, but they are no longer required to bow/curtsey.
Quite right, curtseying and scraping are no longer required in any country, however many "monarchists" still do that. But times change and people are of a much more democratic and equal mindset, so that a formal handshake is absolutely enough to greet even the Q of GB. (who famously said, that she could hear Cheryl Blair's knee stiffen when she said hello).
However the protocol is: commoners to royals.