There are some physiological conditions that may be tied to overall structure of one's hands, however these are not very reliable correlations. For instance, there may be a correlation between finger length and exposure to pre-natal testosterone, which in turn may be correlated to aggression and masculinity (PDF).
Hand-grip strength also showed a correlation to male behaviour in this paper (PDF).
Handgrip strength (HGS) is a noninvasive measure of physical health that is negatively correlated with disability, morbidity, and mortality
rates in adults. Highly heritable, HGS is indicative of blood testosterone levels and levels of fat-free body mass. In this study, we investigated
whether HGS was related to measures of body morphology [shoulder-to-hip ratio (SHR), waist-to-hip ratio, and second-digit-to-fourth-digit
ratio (2D:4D)], aggressive behavior, and sexual history in 82 male and 61 female college students. Results showed that HGS was correlated
with SHRs, aggressive behavior, age at first sexual intercourse, and promiscuity in males but not in females. HGS appears to be an honest
signal for genetic quality in males.
Specifically regarding your question on palm lines. A student at the University of Texas is making a study of the simian line and palm creases, however I have not found the results. In particular, they are looking for (emphasis mine):
The palm lines do not have a direct implication on the success rate of mating and reproduction, nor on development and health, hence palm line pattern is not actively sought for by Natural Selection. Any mutation that causes change in palm line pattern is not specifically selected or rejected because of the palm line pattern, but because of their other effects on other parts of the body or other stage of development.
The student goes on to say:
Statistically significant correlation between the palm line pattern and the disease is looked for using methods from data mining including, but not limited to, artificial neural networks. Our hypothesis of the correlation so obtained is then tested on another large set of people not known to have this disease or not. Those identified with the disease are then verified using traditional methods of DNA testing.
Zano mentioned a Swedish study, and I found this report that does say that there may be some correlation with the simian line.
People with Down syndrome typically have short, stocky bodies with thick hands and feet. Their hands also commonly have a "simian crease", which is a crease in the palm that runs completely from one side of the hand to the other.
However, it doesn't seem to make clear the correlation, and specific genetic cause of that line in this article.
This paper (PDF) mentions the simian line once in 106 pages, however it doesn't offer any useful conclusions.
Although, Columbia University statistics warn against attributing too much in terms of correlation, since it is easy to lie with statistics.
BOTTOM LINE: There may be some correlation; however, the mechanisms and studies are still ongoing. Beware of anyone saying that because of "X" therefore "Y" in this case. As is all too often the case, these things are much more complicated than simple correlations.