If you account for applicant quality in how you measure exclusivity: NSF fellowships, top medical schools, top JD programs, top science PhD programs, many jobs, some country clubs,
The Rhodes and Marshall scholarships come to mind as "most exclusive." They're arguably not "open application" due to age requirements. I suspect YC has an age requirement too, but it is less restrictive (and less explicit.)
If you don't control for applicant quality, then even entry-level jobs are more exclusive than YC. I've been in charge of hiring for a jobs where we made job offers to less than 0.5% of applicants. Which is just to say that acceptance rate alone isn't the right metric.
I think I'm touching on a small sliver of the "most exclusive things" list. The fact that most of the world hasn't heard of YC would also suggest that there are also exclusive programs in other fields that we aren't familiar with.