Personally I would not be in agreement with every person in the country giving their DNA, but I would be in favour with all persons that are arrested having their DNA taken and held on national Database, be it a serious offence or minor offence. Criminals generally start of committing minor offences and then progress to more serious offences.

This is the procedure used in England and it works very well, with a population of over 50 million, there is only around 2 million DNA profiles held on the database, which goes to show that the majority of the population are law-abiding members of the public.

In relation to how it works, a police scene of crime officer finds a sample( blood, saliva, hair, etc) at the scene, the DNA from this sample is then serached against the DNA held on the National database, if this serach results in a full profile hit, then the probability of it not been this person is 1 in 1 Billion!!!! I think i would call this a sure bet.

If you want to know more about DNA database have a look at below link.

http://www.rte.ie/science/forensic.pdf