I am trying to use COUNTIF in Excel to find how many items in a range match the contents of a separate cell. The idea is, the range contains everyone\'s answers
Try removing the quotes and equal sign from "=BU18" - that will indicate that you are passing the value at that cell, which I believe is what you're looking for.
=COUNTIF(C16:BT16,BU18)
Assuming BU18 contains DEN. Your first example ("=BU18") is saying "count if any of these cells have a value of "=BU18", which won't match anything (unless they answered some weird questions :) ).