Suppose a student is applying to a graduate school. Who is typically on the admissions committee? Is the chair of the department on the admissions committee?
At my (large CS) department, the graduate admissions committee officially consists of:
The director of the graduate program. This is a ~3-year rotating position among the senior faculty.
About a dozen faculty members, distributed roughly uniformly across topic areas and faculty rank. The department head is not a member; he's way too busy.
About a dozen graduate student volunteers.
However, our graduate admissions database is open to the entire faculty. Each faculty member is expected to help review applications, and in particular, to identify applicants that they would be willing to advise, offer an RAship, help recruit, and/or recommend for fellowships. We ask each applicant to name a few faculty they'd be interested in working with, so I usually start by reading the applications that mention my name. I haven't been on the admissions committee since 2000, but I still read a few dozen applications every year.
For each round of admissions, each research area (theory, graphics, architecture, etc.) provides a ranked list of applicants for their area to the committee, along with estimates of advising/funding capacity. This usually requires discussion among the area faculty, coordinated by the area chair, who may or may not be a committee member. (I was the theory area chair for several years.)
Final admissions decisions are made by the official committee, but positive reviews from extra-curricular faculty carry a lot of weight. In particular, nobody is admitted without at least three positive faculty reviews, including at least one potential advisor. Decisions are folded back into the database so that faculty can track their favorite applicants' progress, and if necessary, drum up more faculty reviews.
So, in practice, everyone is on the committee, including the department head.
Since this question has somehow come to the top of the queue: in the U.S., in mathematics, the department chair would rarely participate. The person in charge of graduate admissions would be "Director of Graduate Studies in Math.", or equivalent title. This would be a position that would/should involve genuine PR and recruitment work. The old tradition was that the position would be a backwater/sinecure for otherwise inactive faculty. In modern times, the level of energy required to do the job has increased to the point that most faculty could not cope, and do not want such a job, since it would take away from "refereed publications", the baseline for salary and status improvements.
But, of course, grad admissions and policies around this issue have a tremendous impact on the atmosphere in a department. Somehow the internet has made things more intense, more stressed, so choice of people to be around is all the more critical... ironically?
To some degree, the "grad admissions committee" is supposed to represent "all constituencies", but, in reality, this doesn't make much sense, since in the U.S. the thin-ness of undergrad preparation does not allow students to make competent announcements of their eventual interests.
The "real-politick" of grad admissions, involving understanding of the wildly varying undergrad or Master's level preparation around the world, and how those things translate to functioning in the U.S., is not interesting to most faculty, so the responsibility descends to the shoulders of a relative few who've paid attention to the reality, rather than the PR.
Who this is in a given place, and whether it's anyone at all, depends...
In our small department (about the same size as David Ketcheson's), there is no admissions department per se. Master's applications are initially read by our student-services person, who routes the ones passing an initial sniff test to two reviewers (faculty/instructional staff), ideally ones whose specialties align with the applicant's. Reviewers score applications on a rubric, adding a five-point-Likert-scale recommendation (from "definitely admit" to "deny").
A third reviewer may be sought if the original reviewers' opinions diverged significantly. The assistant director of the program resolves any remaining in-limbo applications.
Ph.D admissions, however, go through the Ph.D Committee, which consists of tenured faculty.
In my department of 15 faculty, 3-5 faculty serve on the committee. This usually does not include the chair, but sometimes has. The committee makes final decisions on most Masters applicants, and screens PhD applicants. But promising PhD applications are also reviewed by likely potential advisors before a decision is made, so faculty who are not on the committee also play a major role.