Although I agree with many people in this discussion that the collection of DNA for every arrest is an invasion of privacy, I do not agree that the use of collected DNA should be seen the same way.
Before DNA, law officials used everything they could find at the scene of a crime to narrow the list of suspects. Items such as hair, finger prints, foot/shoe prints, personal affects, weapon, etc. were all used to find likely culprits. If you found red hair, you'd look for red-haired people to question. If you found a foot print that indicated the culprit's weight and height, you'd look for people with those attributes. None of this is at all seen as an invasion of privacy.
DNA is just another set of evidence used to limit the number of suspects. It cannot be used to convict (although, with enough other evidence, it does help). If I were accused of a crime and they had found DNA at the scene, I would gladly turn in a sample so that I could remain free.
I do believe that collecting the DNA of felons or perpetrators of violent crime is acceptable, but only after they have been tried and found guilty. That last part is important. Collecting DNA is much the same as recording the person's name, address, height, weight, outstanding features, and finger prints. I see no difference.
I do not believe that collecting everyone's DNA would be beneficial for anyone. Indeed, collecting that much data would slow the process significantly (think of searching for a "John Smith" living somewhere in the US). If we claim that collecting the DNA of known criminals is an invasion of privacy, then we must claim that collecting ANY data on known criminals is also invasion of privacy.
But... that's just my take on it.