There are three major STEM promoters in the guise of a robotics competition: Offerings from FIRST, competitions sponsored by Vex, and KIPR BotBall. FIRST is the most well known at this point, thanks to excellent promotion by Dean Kamen. And Vex is great. But I think Botball has long thought been historically the best of the three, if the goal is to inspire, teach, and enable students who otherwise wouldn't have had an such opportunity.
BotBall is a shoestring nonprofit which was out very early doing competitions using Lego, motors and sensors, and MIT Handyboards: essentially a middle-school and high-school version of MIT's 6270 class. Botball competitions pit one robot against another and the robots are fully autonomous. Once the lights go on, the robots are completely on their own. Botball doesn't do teleoperation at all. This forces students to think of robots as complete systems of mechanical, electrical, sensory, and computational elements. I think this is good.
But BotBall has a critical additional big plus: it is very cheap. BotBall is a shoestring nonprofit and costs very little for schools to get started, and they work hard to allow schools to reuse most of their kits the next year even as the competition changes, so the rewnewal cost is extremely low. This means that BotBall is a very good choice for Title-1 and other disadvantaged schools, as well as non-school entities. One problem I've seen with some STEM ventures is their high cost, which is then offset by corporate sponsorship for schools. And there are a lot of problems with that model, often resulting in bias in selection of schools, or in kids' educational experience getting sidelined in the name of corporate success. BotBall is not only cheap for schools, but it's so cheap that corporate, private, or academic sponsors can jump in without a need to win at all costs. I myself have funded several Title-1 schools several times as a (mediocre) line item in NSF robotics and AI grants I've received, and highly recommend it.