(Alt title for the specific trope I'm talking about: "Welcome to Adulthood" or "Congratulations For Surviving Your Childhood") Lots of cultures have a special ceremony that marks the transition from teen to adult. It's both a celebration of a major life landmark and an acknowledgment that the celebrant is a part of the mystical society of grownups. In cultures without such a ceremony, other major life landmarks are celebrated instead. (Keeping everything to one trope for now, it might be splittable once we collect enough examples.)
Japan has the Coming of Age Day for reaching twenty and the eating of Red Beans And Rice for a girl's first menarche.
America (and other parts of the Western World) has the Sweet Sixteen; less formally, getting your first car (representing freedom and responsibility), turning the age of consent, losing your virginity, turning 21 (or being old enough to legally drink), and graduating from high school and/or college are also seen as major steps towards adulthood.
Women of high society mark their first formal debut in high society with debutante balls. The Pimped-Out Dress is an important part of this. Also called a coming-out party.
Latin American girls get the Quinceaera ("Fifteen Years") and the Catholic rituals (see below).
Cultural and Ethnic Jews have the Bar (or Bat) Mitzvah at the age of 12, to symbolize that the celebrant is old enough to understand the Torah (the Books of the Law). Being roped in as a performer at a Bar (or Bat) Mitzvah is seen as one of those jobs you have to do to make ends meet, but not a dignified gig, just barely above being a birthday party clown.
Catholics have Confirmation at the age of 12 to, well, confirm that the baptism they were given as infants has lead to becoming a full member of the church. Other Christian denominations have similar rites.
Muslims have the circumcision of both boys and girls (though this is rare) at age 12.
Stone Age societies (real or fictional) are presented as having ridiculously frightening rites of passage involving stinging insects, piercing of nether regions, psychosomatic drugs, and so on and so forth.
Examples:Anime and Manga