Having had a second second child recently got me thinking about the concept of identity. It's a concept we use every day, mostly without thinking about it, but it's not built on a completely solid foundation. The discussion below relates to the US, but I'm sure the story is similar in other jurisdictions.
To get a passport, a driver's license or a social security number, one needs a valid birth certificate. Suppose, for one reason or another you want a second identity. This is illegal and I'm not recommending anyone try it, I'm just interested in thinking about vulnerabilities in systems. Since the government can cross-check with official databases, just forging the piece of paper probably isn't going to work. A method that often seems to be used is obtaining the birth certificate of someone who was born around the same time as you but who died young (and, if possible, in a different state). This "paper chase" method has its disadvantages.
What you really need is an identity that has already been created and maintained, but not used by anyone else - a farmed identity. I'm sure there is a black market for farmed identities, but the question is - how do those identities get created in the first place? That's where the babies come in. If you are a mother with a brand new baby, what's to stop you from going to a doctor and saying "I gave birth to a baby in my house, without even knowing I was pregnant"? (Such things do occasionally happen). The doctor will issue a birth certificate (in addition to the one you already have) and then you have a second identity you can farm for your child (or sell on the black market, if you are so inclined). While most mothers of newborn children probably wouldn't think to do this, I'm sure there are some who do.
Even biometric identity databases can't completely solve this problem unless, whenever a new birth certificate is applied for, the child's biometric information is compared to all the other entries in the database. I'm not sure if that is likely to be practical (given the imperfect nature of biometric data).
One problem with this method is that the mother is now on record as having two different children within a very short space of time, neither of which are recorded as being a twin. This could raise red flags. The answer is for the mother to use a false identity when applying for the second birth certificate. I don't think it would be practical to only give a child a birth certificate after a strong identity check on the mother.
Strongly identifying everyone is a really difficult problem. Should it even be attempted at all? If you don't even try verify everyone's identity, there are certain things you can't do. You can't ban someone from driving, since they could just get a new driver's license under a different name. So if someone is a danger to others on the road, you have to punish them the same way as other crimes - by putting them in prison.
You can't prevent someone from voting more than once by using electoral rolls, so you have to use electoral staining (though I'm not sure if that's perfectly reliable, given the availability of solvents).
You can't give someone large amounts of credit without collateral, since they might just disappear and assume a new identity. I don't think that's likely to be a big problem in practice, since good credit takes time and effort to obtain.
You also can't keep people in (or out) of your country, since they can always obtain a new identity with a clean passport. But national borders tend to be rather porous anyway.