What do the admission committees learn about an applicant by knowing which other programs and schools one has applied to? Does applying to another program which is more prestigious make the applicant seem more serious?
One thing that some programs look at is whether you are likely to come if they accept you. Say you have a 4.0 gpa, perfect GREs, great letters of recommendation, and publications in respected journals from your undergrad research, and you apply to a bunch of the top schools and some mediocre schools. If there isn't something in your personal statement explaining why you are applying to the mediocre school, and that school sees all the other great schools you applied to, that school may not accept you because they assume even if they did, you would surely go elsewhere. Why would a university do this? Well its a waste of money to fly you out, but more importantly when someone gets put on the wait-list awaiting your decline of the offer, that person may accept other offers from schools that did not wait-list them. I have been told first hand by members of admission committees that the "where else did you apply to" question is used at least partially for this purpose.
Additionally, at the university administration level, they like to keep track of which universities they compete with for students. I have seen Universities present statistics on how many students reject their offers, and which universities they end up in. So the question is also probably there for statistics tracking purposes unrelated to the admission process. This is a potential reason why even the top schools will ask this question.
Some things I (as someone sitting in academic admission committees) would learn from this question is
- is the person flexible (willing to move)
- Did (s)he just apply to some randomly selected institutions or is there a clear dedication to one field
- Who are my main competitors (and this might be the true reason for this question).
I concur with OBu that competitive intelligence is the major reason for this question, but there is one individual-level strategic concern: financial aid. It's sometimes possible to guess what kind and amount of aid a given applicant is likely to attract. That leaves us with the question of whether we can or should match it.