It looks like the idea that people grow more conservative as they get older is just a myth, according to researchers at the University of Vermont. On several major issues, people even tend to become more liberal as they age, specifically regarding gender equality and tolerance of viewpoints such as atheism and communism. Areas in which people do tend to become more conservative are viewpoints concerning extramarital and premarital sex.
The study also acknowledges that some changes towards more liberal viewpoints can be attributed to older people starting from a more conservative position originally than young people today. For example, older people today have made much more dramatic changes in a liberal direction regarding race relations than have young people, because the older generations may have grown up under segregation and outmoded stereotypes.
This helps put to rest the view, common among many on the American right at least, that liberalism is a phase that is grown out of. One particularly loathsome cliche is "If you are a Republican when you're young, you don't have a heart. If you're a Democrat when you're old, you don't have a brain." It's clear many people find that experience and reflection help to liberalize their worldviews.