The short answer to this question is yes, but the long answer is much more complicated. There is, in fact, an entire field dedicated to the study of genetic personality traits and behavior; this field is known as behavioral genetics. Scientists in this field combine a study of genetics, psychology, and ethnology to study behavior trends in various populations of humans and animals. As the mysteries of the human genome are unraveled, this field of study is rapidly expanding.
When looking at genetic influences on personality, it is important to remember that genes alone are not responsible. In the first place, genetic personality traits are polygenic, which means that they involve multiple genes, not a single gene. Therefore, study of these traits is extremely complex, since scientists still do not fully understand how these genes interact with each other, let alone how they interact with other genes. In addition, environmental influences can have a major impact on personality, although these influences may interplay with someone's genes.
People who study genetic personality traits look at large populations in an attempt to identify shared characteristics. This is where ethnography is important, as scientists want to be sure that they are getting an accurate sample, to ensure that their work is valid. Some studies have also been extremely involved, lasting for many years in an attempt to look at multiple generations and environments. Study of animals has revealed numerous personality traits which are clearly genetic, as they may be species-specific adaptations to unique environments.
In humans, a number of genetic personality traits have been identified. Scientists have observed that things like mental illness and alcoholism appear to have genetic links, with many families exhibiting statistically unusual incidences of these conditions. Personality traits that are passed down may also be more subtle; some families, for example, seem to pass down a general trend of anti-social behavior, although it may be difficult to pin down specific behavioral tics and trends.
It is difficult to study genetic personality traits ethically, since so many factors can come together to influence someone's development. Scientists need to rely on observational study as manipulation of the human environment is generally considered unethical. Twin studies have proved particularly interesting for psychologists who study these types of personality traits, since twins may develop into remarkably similar people despite being separated at birth. Two twins who have never met, for example, might both decide to become firefighters, suggesting a clear genetic link between their personalities.