There are two general reasons why privacy is important.
The first is that privacy helps individuals maintain their autonomy and individuality. People define themselves by exercising power over information about themselves and a free country does not ask people to answer for the choices they make about what information is shared and what is held close. At the same time, this does not mean that public policy should shield people from the costs of their choices. American privacy allows our many cultures and subcultures to define for themselves how personal information moves in the economy and society.
A second reason that privacy is important is because of its functional benefits. This area has been especially slippery for policy-makers because they have often use the term "privacy" to refer to one or more of privacy's benefits.
For example, anonymity and pseudonymity protect the privacy of people's identities, which has the functional benefit that someone may speak at a political rally — or go to a bar — and not have to answer later to political opponents or unwanted suitors. Anonymity and pseudonymity lend to both privacy and these safeguards for safety and peace of mind.
Another example were the word "privacy" often substitutes for an important
benefit of privacy or confidentiality is identity
fraud. Very commonly today, proposed legal limits on uses
of Social Security Numbers or account numbers have been touted
as "privacy protection."
Few people care about privacy in their Social Security Numbers for its own sake or because of autonomy or individuality. Nearly every American has been assigned such a string of numbers, which makes the fact perfectly mundane. The numbers themselves are mundane too.
The aim of limits on SSN use is a functional benefit of "privacy": crime control. Keeping identification and account numbers from the general public is analogous to keeping car keys in one's pocket or purse rather than in the ignition. Such measures make it practically more difficult for criminals to steal our cars or access our accounts.
There are many more complexities to the privacy issue. Unfortunately, few today have yet sorted them out.
Understanding Amy Boyer's Law: Social Security Numbers,
Crime Control, and Privacy, Privacilla.org (December 2000) in PDF format. Also available in html format.