Planes: Historicaly, most of the time, when choosing where to put flight instruments and controls, being a choice, left side, so that's where the pilot sits. He can reach and see what he needs.
Even in more modern aircraft, where there is much more redundancy in instruments and controls for the right seat pilot, most of the time, serious systems circut breakers are closest to the captain on the left side.
Helcopters. The advancing blade on the main rotor creates more lift then the retreating blade in forward flight. The pilot sits on the side of the advancing blade to counteract the roll tendancy at higher speeds.
In aircraft where there is no intention of a single pilot captain, then certainly systems, controls and the design of the aircraft are much more blended to accomodate comfortable flight control from either side.
Certainly exceptions do exist, and varies from manufacterer, make and model, as someone's idea of where to put CB panels, controls, and instruments vary.
I could make the joke, that because most of the world drives on the right side of the road(the way it should be) that is why the pilot sits on the left side...more akin to driving a car, visualy more similar and comfortable on taxi ways, up in the air ect.