One Shinto tradition that seems less well-known outside Japan is that of “Yakudoshi”. These are years (doshi) when people are thought to be particularly susceptible to misfortune (yaku). For men, they happen at the ages of 25, 42, and 61, while for women they are at 19, 33, and 37. These are both measured by “counted years”, according to which you are born at the age of one, and become two at the first January 1st after that.
There are a lot of theories about the original meaning of these years, and why they are when they are. The most popular theory is that they are ages when important changes happen, and that has recently received scientific support: people apparently age in spurts around 44 and 60. Forty two in Japanese is “shi ni”, which means “death”, and 61 marks the beginning of your second time around the Chinese sexagenary cycle, so there are good reasons to choose those precise years if there are noticeable changes that happen somewhere around them. The different ages for women are probably related to childbirth in premodern cultures, and the first age for both sexes is roughly when someone would be recognised as “fully adult”.
However, there is also a theory that the “yaku” did not originally mean “misfortune”, but rather “responsibility”, and that this was a year in which people were required to serve the kami in some way.
In any case, the standard Shinto response these days is to encourage people to visit their local jinja and have a purificatory prayer offered. Many jinja post lists of these years, and the birth years that are currently affected, in the window of the jinja office. The full custom is to have the purification done the year before and the year after, as well as in the main year. I can see obvious reasons why jinja would encourage that, but there might be deeper ones as well. As with most traditional customs, there is no general agreement on the reasons for everything.
This is less common than the Shichigosan (7-5-3) ceremonies for children, but it is not a niche thing — as I say, many jinja display lists, and I have vague memories of seeing statistics saying that about 10% of Japanese have the purification, or maybe pay attention to the years. (As I say, vague memories.) People often have the prayer done early in the year, but you can do it any time in the year, although the later it gets, the less of the year it covers.
A couple of days ago, my daughter and I went to our local jinja to do her first one. The priest (who remembers the prayer for her safe delivery) expressed some surprise that she had reached that age already. We would have done it earlier in the year, but fitting things into a high school student’s schedule is not easy…