There are two things my grandparents used to do that I expressly associated with adulthood. The first was my Nanny wearing a nice anklet -- I remember telling her I wanted one when I was about 6 years old and her responding that I would have to wait until I was a big girl. The day I graduated from grad school I bought me an anklet!
The other is that my Papa would always mix cereal -- really 'adult' cereal like Raisin Bran and Fiber One. Man did I think that was gross! Well -- a lapse in judgement led me to purchase a 3-pack of fruit loops at Sams a few weeks ago. That stuff is terrible. I was hungry by 9am every day! This morning I went downstairs and mixed Raisin Bran and granola. I guess I'm a real live adult now!
On a more serious note about growing up, you should read this article: The world is full of boys who can shave. It's so interesting to me! The basic premise of the article is that the transition from boyhood to manhood is typically indicated by 5 sociological variables: leave your parents home, finish your education, start a career, marry a woman and, finally, start a family. Those variables are all messed up in our culture today...occurring out of order and often not happening at all (think Failure to Launch). Many of the same principles apply to women as well...but I think to a much lesser and different degree.