I am definitely far from being an expert, but @hebegebe is, and he is right that the programs like RSI that are not shy about the matriculation stats of their alumni are also clear about their own selectivity.
Here’s a Forbes article written by the current RSI director (he wasn’t at the time it was published):
There is a little-known secret method of getting a student admitted by top colleges and universities.
Getting perfect grades and admissions test scores is not enough to get into the most selective colleges and universities. College admissions offices want more than just great academic performance. They want students who go above and beyond.
There are certain summer programs and competitions that act as a mark of excellence. Students who attend these programs or earn the highest rank in these competitions are much more likely to get into the most selective colleges and universities.
One of these programs is the Research Science Institute (RSI) run by the Center for Excellence in Education (CEE). CEE was founded by Admiral H.G. Rickover and Joann P. DiGennaro more than 35 years ago to keep the U.S. strong in science, mathematics, technology and engineering. The RSI program is free to participants.
Most RSI alumni, known as Rickoids, enroll in some of the nation’s most selective colleges and universities. A third (33%) attend Harvard, 22% attend MIT, 10% attend Stanford, 5% attend Princeton, 5% attend Yale, 3% attend Caltech and 2% attend Duke.
There’s just one catch, which is getting into RSI.
RSI is more selective than MIT, Stanford, Harvard and all other colleges and universities worldwide. Only about 2% to 3% of U.S. applicants are admitted to RSI each year.
He then goes on to list some other well-regarded summer programs and high-school competitions.
What is common to many highest-caliber programs is that in addition to their selectivity they are free to participants - though there are certainly exceptions (MathCamp, for example).
In any case, in the spirit of “applying sideways” I would only encourage my child to participate in a program they were genuinely interested in without regard for the admissions prospects. If the main motivation for doing anything in high school is to better the college admissions chances, it is very likely to result in a disappointment.