I'm against anything like this, and here are some possible problems with having a DNA database:
What if someone leaves a DNA sample quite innocently at a crime scene? For example, someone has a nosebleed or sneezes or something at a place where, an hour later, a crime takes place where DNA evidence might be relevant. Isn't there a danger of the innocent person getting convicted, especially if DNA evidence is seen as irrefutable?
Surely the people most in favour of having their samples filed would be those least likely to commit crimes. If so, why do their samples need to be on the database in the first place!?
Also, I might be wrong but as far as I know, if you are arrested, have a DNA sample taken and then get cleared of any charges, your sample remains on the database whether you like it or not. Where's the justice in that?