What is the likelihood of not being accepted to any of my match/reach schools? Does it happen often?

I am the leader of four student organizations, a high-ranking member of two others, and the captain of two varsity teams. I am also ranked 2/103 in my class, scored 1540 on my SAT, and took AP Chemistry, AP Biology, AP Spanish, APUSH, AP BC Calculus, and an advanced year-long science research course. I attend a college preparatory school in Massachusetts.

I plan on applying to Brown as my top choice, Tufts (my brother will have graduated), Northwestern, Pomona, Stanford, UPenn, Harvard, Wesleyan, Northeastern, UMass, BU, Emory, Haverford, Brandeis, Harvard, and Princeton.

I presume that UMass, BU, and Brandeis will be somewhat safeties for me and the others are reaches and matches. Is it rare or common that applicants are rejected to all of their reach/match schools and are left with one or two safeties to choose from?

What is your GPA? You didn’t include that.

Given that you have an in-state school as a safety in addition to two others, I think the likelihood of you ending up with zero options is slim. However, if you look in the “Admissions Hindsight” subforum, you will see it is possible to be rejected from all reaches/matches- I recall one kid with a perfect GPA and 2300+ SAT and strong research ECs get rejected from every single school but UArk.
It is not common, but it can happen that you only get to go to a safety. That’s why you should make sure you apply to safeties you actually like (and if possible have one that is rolling/EA, it makes the year easier if you know you have a spot somewhere in december).

Make sure that your safeties are affordable and that you actually like them, as well as being assured for admission.

BU and Brandeis are safeties for none. Your assumption is not a sound one. Your list is filled with primarily reaches for all and a couple of matches. You have 9 colleges with sub-20% acceptance rates, and the rest, except U Mass, are in the 30’s. You need safeties, unless you are happy to attend U. Mass.

It can be very likely depending on how high the reach. Does your school use Naviance?

You are going to be fine - I count 7 schools you are more likely than not going to get into, IF you show enough interest. I tell my kids to show more interest at their safeties and matches than for their reaches. Make sure to hop on a plane and vist schools like Emory. I’d also consider dumping BU, Brandeis and Northeastern in favor of Rochester, Oberlin, Kenyon, Carleton and/or Case. You’d have better admissions odds at those schools and they are arguably a little stronger.