In order to count the people, this week's sidrah famously states, each person is to give a half shekel and that is to be counted. The words from the sidrah cited above constitute the most obvious biblical source for the halachic prohibition, codified by Maimonides and others, against directly counting Jews.
Our reluctance to count fellow-Jews by number spans our entire history, finding fascinating contemporary application in halachic issues surrounding the Israeli population census (for example see J. David Bleich, Contemporary Halakhic Problems Volume 3, chapter 13).
Many have suggested that a direct head-count is deeply flawed because it relates to every person simply as an anonymous number. We feel an instinctive horror at the Nazi practice of reducing human beings, each a whole world in him- or herself, to mere numbers. When we do count individuals, we count them by name - bemispar shemot, as the Torah says in the Book of Numbers (1:2).
A further problematic aspect of a direct counting of Jews is that it involves a misplaced emphasis on numerical strength. We are a small people, and our miraculous survival over the millennia has never been achieved by sheer quantity. "Not because of you are many compared to other peoples did God desire you... for you are the smallest of all peoples" (Deuteronomy 7:7). There are several good arguments for the Orthodox world being more welcoming of converts, especially in Israel, but the idea that we need "more numbers" is not, in my opinion, one of those arguments. In Judges chapter 7, God repeatedly tells Gideon that he has too many soldiers. Jewish strength lies in faith, humanity and spirituality, qualities less concrete than numerical power, but more durable by far.