I think in some spiritual traditions there's a lot of stuff for children, so you can begin them early. While some take a real spiritual turn at a young age, for me the turn towards spirituality came 11 years ago when I was 34.
My kids are learning two spiritual traditions. Their mother is Catholic. They have sunday school where they can teach the children the traditions. In a way, I see sunday school as a kind of cultural thing, a family thing. Learning about religion at a young age isn't a bad thing, even if it's not my tradition. As a Buddhist in America, I am very aware of other spiritual traditions.
I do like to share my tradition with my kids. Last night we watched Little Buddha for the first time. I've been waiting to show that to them. I think they were OK with seeing it at age 7 and 9. This movie splices the story of the life of the Buddha with a narrative about a boy who has been recognized as a Tulku in the Tibetan tradition. The family is skeptical because they are not Buddhist, but they go on a journey of discovery too. I've learned a lot about the Tibetan flavors of Buddhism, but I don't practice in that tradition, so in a way it's a weird kind of introduction. I'm like the guy in the movie who ends up wishing he believed in reincarnation.