Once you decide to commit a crime you should lose a lot of the privileges that this great country has given you. If the government had a database with all of the criminals DNA they would be much more likely to catch all the rapists and murderer's. It would also solve a large amount of burglary's.
Yes, governments should keep a DNA database of criminals, because it solves crimes. Most criminals do not offend just once. Most are not caught the first time they offend. Keeping a database can help solve crimes, which will prevent other people from becoming victims. When a person commits a crime, they give up their privacy to not be in the database.