Question special

There are many factors which applicants consider throughout the interview trail and while creating their rank lists. One of the most common concerns is the perceived reputation or "tier" of a program. This question will be broken into two parts: first, what factors influence the reputation of a program (eg research output, national prominence, notable faculty/alumni)? Second, should the reputation of a program influence an applicant's decision, and if so, why? Please discuss how the answers to these two questions can vary per specialty.