These are some programs that are popular among high school students. This is by no means an exhaustive list of nationally recognized programs.
Boy’s/Girls States are programs that offer citizenship and leadership training during the summer for high school juniors. The American Legion runs them.
ISEF/Siemens are two scientific research competitions that award students who present their research with scholarships and recognition.
The Paige program is a congressional program that allows you to intern at the office of a U.S. government official. There is an application process.
There are various Honor Societies that circulate throughout high school. You should research the ones that are genuine and not scams. The most popular one is the National Honor Society.
RSI is a six-week program offered by MIT that deals with the STEM subjects.
SSP is a Harvard university program that allows high schools students to take classes on campus during the summer. Some classes offer college credit.
WTP is a program that MIT offers to spark the love of engineering in high school girls.
Columbia Science Honors Program is a program that allows high school students to take classes at Columbia after going through an application process.
HSHSP-MSU is a program at Michigan State University that gets students involved in research.
MIT-ES is a MIT program for minority students involved in science and engineering.
The Center for Critical Immunology offers high school students various medicine related camp opportunities at Stanford University.
EPGY is another Stanford program that allows high school students to take classes (both high school and college level).
NFL is a forensics league that pits the top national debate and speech students against each other.
SUMAC is a Stanford camp for mathematics that takes place in the summer.
FBLA is a student business organization that offers competition to students looking for public speaking and entrepreneurship experience.