Will to me we have come a really long in this type of thing. Just think in the early days and ages of time if you did a crime and left DNA evidence than you could of possiable got in away with the crime if that was the only way that they could of proved that you where the one that did the crime.
To answer this all we have to do is look at the large number of cold cases that have been solved with sometimes decades old DNA, or the number of people that were falsely imprisoned who have had their names cleared by new DNA techniques.
While there is no national database of DNA as of yet, the law does allow for DNA to be collected from those who are already convicted inmates, and that information is stored and crossmatched with other evidence. Hundreds of cases have been cleared in this manner as well.
Criminals must really be careful when they go about their evil ways in the 21st century. Leaving something as simple as a stray hair behind at the crime scene can be proof enough for a conviction (although it may be insufficient in the ongoing Casey Anthony case). Saliva, blood or other bodily fluids are just as damning as fingerprints now.
I would have to say that you are right. Before the use of DNA, the best way to identify someone was through fingerprints. Those are useful, but they are very limited in their usefulness. There are so many instances in which DNA is left at a crime scene but fingerprints are not.
The only drawback to DNA is that there isn't the sort of national database of DNA that there is of fingerprints. If you find a fingerprint at a crime scene, you can run it through the system and find out (potentially) who it is. That's not possible with DNA.