Where I am, we have one number for tax, one number for health care, one number for drivers license, one number for passports, and nobody uses any of them improperly. But they are all secret, and not known to anyone who doesn't need to know it.
SSN is supposed to be secure, but everyone has it and it isn't secure.
Exactly, it's the same thing in Spain. I have one DNI number (Documento Nacional de Identidad, National Identity Document), a drivers license number, and a passport number (used to be the same as my DNI, but now that I live in Japan the number has changed). Spain also has a number for tax purposes, the NIF (Número de Identificación Fiscal, Tax Identification Number), but it's just the DNI + a letter which is a function of the DNI numbers, sort of a CRC.
We don't go around telling our ID numbers to everybody (unless you're a business, then you're required to), but they aren't exactly secret either. The government itself routinely makes them available when publishing documents about student grants, lawsuits, etc, as in this one.
If you know my full name you can easily find out mine searching for "firstname lastname1 lastname2 NIF".