I've been reading through Peter Shirley's excellent Ray Tracing in One Weekend and implementing the ray tracer in Scheme. It would be a great project for a teenager interested in programming. As the father of a daughter who turns one in a couple weeks, I have a long way to go before she's a teenager, and I'd love to introduce her to fundamental concepts of programming as she grows up.
My daughter just recently took her first steps, so it's probably going to be awhile before she writes her first lines of code. For you parents who are further along the parenting path, when did you start introducing your kids to programming? What activities such as certain games or toys did you find reinforced programming concepts without involving actual code? How do you teach young kids about programming?