It might be time to get Gattaca-level paranoid about leaving your DNA all over the place, as geneticists are getting closer to being able to determine what your face looks like simply by analyzing your genetic code.
Whether you believe in nature or nurture, the physical structure of your body is defined almost entirely by your genes. There will be some variation, of course, depending on your age, your weight, how well you take care of yourself, and how many times you've gotten punched in the face, but things like the space between your eyes, the height of your cheekbones, and the size of your nose are all preset and encoded in your DNA. This is why twins can look identical, and also why siblings can look similar: it's shared genetics.
Methods for figuring out eye color, hair color and skin color from DNA are fairly well established, and geneticists are now working on the next step, which is extracting the locations of "facial landmarks" from a DNA sample and using them to reconstruct the shape of someone's face from their genetic code alone. We should stress that this research is very, very preliminary, but we should also stress that there were some results, albeit small effects correlated with a limited number of genes.
For example, the researchers found that a gene called TP63 was a predictor of the gap between the centers of each eye socket being narrower by about nine millimeters. A gene called PRDM16 is associated with nose width and nose height, while a gene called PAX3 influences the position of the bridge of the nose. All of these things are measurable and predictable, and don't take anything more than (say) a sample of blood from a crime scene.
Again, all of this research is very preliminary, and we don't have information about nearly enough genes to accurately create an entire facial picture. Yet. But this research shows that it will likely be possible to at least create a sort of artist's sketch of someone's basic facial structure, eye color, hair color and skin color, just from a sample of their DNA.