Biometric passports with fingerprint data are common in many EU countries. The fingerprint is used to verify a person's identity, so in a way it's used as both a username and password.
Allowing the state to capture and store something very private to every individual is not without controversy. A few years ago, a German man called Michael Schwarz had his application for a passport rejected when he refused to have his fingerprints taken. He took the matter to the European Court of Justice (ECJ). In October 2013, the ECJ ruled in favour of fingerprinting for passports. The ECJ agreed that fingerprinting was a privacy intrusion but that this was outweighed by the need for security and protection against fraud. Strictly speaking, the fingerprint data should only be held in the passport, not in a central database.
Whether you agree or not with fingerprint capture will probably be influenced by how much you trust the authorities in your country. And of course, many countries collect fingerprints from visitors entering their country.