According to Wikipedia, citizens of Ukraine can/must have biometric passports [doesn't imply retaining biometric information].
Accroding to the US Library of Congress, biometric data collected for production of passports is also retained and may be used by law enforcement agencies in Argentina, Australia, Brazil, France, Israel, New Zealand, Ukraine, and the USA.
This may — of course — gradually create creeping de-facto databases of a large part of the population (citizens who travel).
This practice is prohibited by law in Germany, Sweden, and South Korea.
According to wikipedia, Ukraine has a compulsory identity card.