I'm 44 years old. I've been doing family history and genealogy since before I was 20. In all of that time, I've always been one of the youngest, if not the youngest, of any gathering of genealogists I've attended. It seems to be a hobby of the older folks, although there are exceptions. By the time we get old and interested in family history, we don;t have enough time left to do all of the research and organizing and publishing that needs to be done. Sometimes it's hard to find anyone in the next generation who is interested enough to which we can pass the task.
Recently I was made aware of Jennifer Holik-Urban's website, Genealogy For Kids. The blog is written in language that makes it more readable for kids while not dumbing down the subject matter. It presents ways in which kids can begin researching their own family history from information sources readily available to them, including interviewing parents and grandparents, with sample questions given.
I believe kids need a sense of where they've come from in order to know which way they should be going. Family history is a good way to encourage that. Genealogy For Kids is a great resource for getting kids started!