In Dutch and German there is the expression ‘sitting on someone’s green side’. That is the same as on someone’s left side, so sitting on the side of his or her heart. Who ‘sits on the green side’, is closer to the heart of the other. Related to this is the expression ‘not being green about something’, which means ‘not being fond of something’.
Heller (1989)

Stenciled hands at the Cueva de las Manos in Argentina. Left hands make up over 90% of the artwork, demonstrating the prevalence of right-handedness.

(About the primaeval worm, our ancestor of 590 million years ago.) Put our front-rear asymmetry together with our dorsal-ventral asymmetry and we have automatically defined a left side and a right side. But unlike the other two axes, we find no general reason to distinguish the left side from the right side: no reason why they should be anything other than mirror images. Danger is not more likely to threaten from the left or the right side, though it may well be more likely above or below. The prettiest real life example (of an exception) I can think of is the wonkey-eyed jewel squid of Australian waters, whose left eye is much larger than its right. It swims at a 45-degree angle, with the larger, telescopic left eye looking upwards for food, while the smaller right eye looks below for predators. (other exceptions: the wrybill, the fiddler crabs). Trilobite fossils often display bite marks, indicating narrow escapes from predators. The fascinating thing is that about 70 per cent of these bite marks are on the right-hand side. Either trilobites had an asymmetrical awareness of predators, like the wonky eyed jewel squid, or their predators had handedness in their attack strategy. But those are exceptions, mentioned for their curiosity value and to make a revealing contrast with the symmetrical world of our primitive worm and its descendants. Our crawling archetype has a left and a right side which are mirror images of each other. (Dawkins, 2004)

Thinking about time is metaphorically grounded in knowledge about space, where past is to the left, and the future to the right. When choosing an object with the past (vs. future) in mind, a given object is more likely to be chosen when displayed on the left rather than the right.

Charles Y. Z. Zhang and Norbert Schwarz (2011) 

When leaning forward to kiss to a romantic partner, individuals tend to direct their kiss to the right more often than the left. When kissing friends and family, most people lean to the left. Studies were administered in countries with official languages in English (Italy, Canada), Hebrew (Israel), and Arabic (Palestine). They have consistently demonstrated this kissing asymmetry. As for why romantic couples tend to kiss to the right, the researchers think previous research into brain function might hold the answer. Couples entering into new romantic relationships show heightened activity on the left side of their brains, which might guide them to make more rightward kisses. Our brain is split in two: a left and a right hemisphere. Activity in one hemisphere often makes us move in the opposite direction. The emotional center is in the left hemisphere. The stronger your feelings, the more you will move to the right. (Sedgewick & Elias, 2016)