Not particularly, no. I don't really mind the government maintaining a DNA database.
I would like it if they shared the data with the NIH, and I think that work on mapping the human genome is so very important that we can't trust private enterprise to explore all of the possible directions in which it could be taken.
I mean, what is the government going to do with my DNA? Clone me? Invade my privacy by finding out what diseases I'm vulnerable to?
I reject arguments that innocent people have nothing to fear from invasions of privacy, but objections to this don't even seem to be based on one of those.