Like other elements of boating, the placement of the steering wheel is based on both ancient customs and practical concerns. Steering on the right-hand side is likely as old as boating itself.
Modern Explanation
According to the column "The Straight Dope," the steering wheel is on the right side of power boats for mechanical reasons. Boat propellers spin clockwise and the torque on the propeller caused the right side of older model boat hulls to rise out of the water. Boat designers placed the steering wheel on the right so that the weight of the boat's operator would keep the boat even in the water.
Origins
The steering apparatus was on the right side of boats long before the invention of engines and propellers, however. The earliest boats were propelled and steered by paddles. Right-handed paddlers would naturally steer from the right-hand side of the boat. Since the majority of people are right handed, steering on the right gradually became customary.
Starboard
According to the United Kingdom's National Maritime Museum, as larger boats developed, the paddle was gradually replaced by a large oar permanently attached to the right side. Anglo-Saxon sailors called this device the "steorboard" which gradually became "starboard". The steering apparatus was eventually placed in the center of the ship's stern but the term "starboard" remained the name for the ship's right-hand side.
Port
Today the left-hand side of a ship is called "port". However, in the early Middle Ages, Anglo-Saxon sailors used the term "baecbord" which may have come from the fact that the sailor steering the ship had his back to the left-hand side. In later times, sailors used the term "larboard" which may have been derived from "ladderboard", meaning the left-hand side of the ship where passengers and cargo were loaded ('laded') in order to avoid crushing the "steorboard". In the 19th century, "port" was adopted as the term for the left-hand side because of confusion caused by the similar sounding words "starboard" and "larboard".