There are many contest and competition programs to encourage young people in STEM learning. Many of these are well designed and offer great incentives for students and coaches. However, they are also highly proscriptive and demand a lot of adult and student time. This is one of the reasons that they tend to be dominated by higher income participants. Most program organizers are aware of this concern and have been making efforts to reach underserved populations. The Team America Rocketry Challenge opened its entries to non-school groups and ended up having its national winners come from a rural 4-H club.
I am starting to build a wiki page with some more examples of competition programs. Feel free to add more information.