Right handedness: mothers tend to hold their infant babies in their left arms, because this brings the baby into contact with the mother’s heartbeat. This is somehow important for the baby. For example, study in hospitals showed that newborn babies exposed to the sound of a heartbeat cry about half as much as those not exposed to the sound.
Therefore the mothers tended to hold the baby in the left arm thus freeing the right hand to do things, and over time right handedness was encoded generically. Further evidence for this is that even left handed mothers hold their infant babies in their left arm 78% of the time.