A recent NYT piece by Amy Harmon highlights a law-enforcement practice called "surreptitious sampling," which refers to the collection of an individual's DNA without their permission or knowledge. All of us are leaving traces of our DNA all over the place, all the time: on drinking glasses, kleenex, soup spoons, cigarette butts, etc. If the police wanted a blood sample, they'd have to get a court order; but these discarded or overlooked materials may be gathered by US law enforcement agencies--without probable cause or any oversight from the courts--and used to match samples collected in criminal investigations. If the DNA from the murder scene matches the DNA on your soda straw, you're in big trouble.
At the moment, there's no legal barrier against the Feds' deciding to build a national database of our genetic information to be used for law enforcement purposes. The FBI already has a database of genetic information from convicted criminals, and it has lobbied to make the database more inclusive (eg, to retain samples/data from people who have been arrested but not convicted).
In the UK, a national DNA database has been built that contains genetic information on more than 5% of the population (compared with the FBI's collection on 0.5% of Americans). There's been substantial debate in the UK about the legality and propriety of the resource: you can read more here, here, and here, for example.
Lots of people--including health researchers, pharma companies, insurers, employers, and law-enforcement agencies--would like access to huge datasets of individuals' genetic information. Once such repositories are built (and they are already being built), arguments in favor of a centralized resource are sure to follow, citing efficiency and cost-savings benefits. There are (imo) important privacy and civil liberties reasons to resist such developments.