Left-handedness used to be associated with criminality, and researchers are still unclear as to whether and why there are slightly more lefties among criminal populations.
More recent research associates left-handedness with "divergent thinking," a form of creativity that allows you to come up with novel ideas from a prompt — at least among men.
In her review of a 1995 paper, New Yorker reporter Maria Konnikova writes:
The more marked the left-handed preference in a group of males, the better they were at tests of divergent thought.
Left-handers were more adept, for instance, at combining two common objects in novel ways to form a third — for example, using a pole and a tin can to make a birdhouse. They also excelled at grouping lists of words into as many alternate categories as possible.