Our government is (or will be) in control of our health care. If you are genetically predisposed to (or even worse guaranteed to get) cancer or heart disease, should we really spend the money to keep you healthy? What if we discover a genetic link to mass murdering psychopaths, should you be institutionalized before you hurt someone in the interest of public safety?
Solving a crime is one thing, but what else can, would, the information be used for. It could almost become like searching every apartment in a complex because a robbery occurred at one of them.
As for comparing DNA to fingerprints (in regards to booking prisoners) it is not the same. Fingerprints are taken during the booking procedures, not for the purpose of investigation, but for identification (making sure that the prisoner on trial is the one accused, not his twin brother). Once prints are legally "in the system", they can later be used for investigation. The original legal justification for obtaining fingerprints was actually for the protection of the prisoner, using the data to solve a different crime was just a “bonus”. DNA can not, with the present technology, serve the same identification function because testing and comparison is a lengthy specialized process. Its sole current purpose (in the criminal system) is investigative, and should (in my opinion) be held to the same 4th amendment standards as a search of your home (probable cause needed). Just because you got drunk in a bar and cussed out a cop in Boston is not, in my opinion, reasonable cause to suspect you might have committed a rape in California in 1986.
As I said below, I don’t object with the current decision, but I think it does create a situation that is ripe for abuse.