According to Wikipedia, citizens of India can/must have biometric passports [doesn't imply retaining biometric information].
According to wikipedia, Gambia and Iraq seem to have compulsory biometric databases for all citizens (This is only a partial list. For example: Pakistan isn't mentioned). In India it is not compulsory, and in Israel — it's considered to be at a "pilot" stage, so citizens can still refuse to submit their biometric data.
In making Aadhaar mandatory for filing taxes and securing core taxpayer identity, the government has openly gone against a Supreme Court order from last year that explicitly stated that the Aadhaar Card scheme is "purely voluntary" and cannot be made mandatory until the court has decided on this.
Aadhaar's use, by no means, is restricted to government agencies alone. A growing number of private financial institutions are now fulfilling their "Know Your Customer" or e-KYC formalities by making Aadhaar compulsory. The government is also in the process of making Aadhaar the basis of all financial transactions.