Identity document wiki article. I do carry my ID everywhere. Besides being a legal requirement -though no police officer ever asked me for it so far except at the border when visiting countries we don't need a passport for- I needed it whenever I took an exam, competitive or not, opened a bank account, took a loan, I need it whenever I pay by check or whenever I go to the bank to withdraw a new checkbook if the guy doesn't know me. Besides stating my nationality, on my ID there are my photo, full name, date and place of birth, height, address + the date and place of release, so no big secret. As far as I remember they take our forefinger prints but they don't show on the ID -they used to.
Anybody can be easily traced as soon as they have credit cards and/or cell phones... so much for freedom!
Carrying an ID doesn't mandatorily mean police harassment. IMO, when people are twisted enough to harass you just for the sake of it they usually find a legal way to do it, ID or not.