My school had a chapter of NHS growing up, and they had this big ole assembly where the whole school (about 200 of us K-12) attended to see the handful of new members. My class only had like 2 inductees, but my sister's class had 8 or something.
In University honor societies aren't as centralized and you can pretty much find one (or more) for each major or department. There are even some which are a bit more..nefarious. Like the National Scholars Honor Society, which sends out blanket post cards to all college students or campus mail centers with a name like 'magna cum laude", which is a title handed out by the institution and cannot be bought with a "membership fee".
I'm a member of an honor society for Political science, Pi Sigma Alpha, and I was notified of eligibility by a faculty member of my university based on my GPA.