There are, of course, two styles of polarized plugs in the US.
One style which some posters refer to has three plugs, one of which is round -- those three plugs are "hot", "neutral" and "ground."
However, as the asker noticed, SOME US plugs are two-prong polarized. In these plugs, the right-hand-plug is larger than the left. The right hand plug then is "hot" and the left is "neutral." (These are called "type B" plugs.) The older style had two narrow blades and are refered to as "Type A" plugs.
Why polarize plugs? Because in an effort to hold down costs, the makers of some electronic equipment used what is called a "hot chassis." This was common in low end radios and televisions, and extended to other appliances. In those cases, while the appliance would WORK properly with the plug inserted either way, if the plug was in one way, it was safe to touch the bare metal parts of the equipment and the other way, it was most assuredly NOT safe to do so. So, the National Electrical Code people, and the equipment manufacturers came up with the polarized plugs.
This standard is enforced as part of the standards of the National Electrical Manufacturer's Association (NEMA) and adopted by 38 other countries, this simple plug with two flat parallel pins, or blades, is used in most of North America and on the west coast of South America on devices not requiring a ground connection, such as lamps and "double-insulated" small appliances. NEMA 1-15 sockets have been prohibited in new construction in the United States and Canada since 1965, but remain in many older homes and are still sold "for replacement use only". Type A plugs are still very common because they are compatible with type B sockets.
Early designs could be inserted either way, but modern ones prevent the neutral pin from being inserted into the live socket by making it wider than the live one, referred to as a polarized plug. (Note that this is not the same as positive/negative polarization in a direct current system.) New polarized plugs will not fit in old type A sockets, but both old and new type A plugs will fit in new type A and type B sockets. Some devices that do not distinguish between neutral and live, such as sealed electronic power supplies, are still sold with both pins narrow. When attaching a new polarized plug to a cord, it is useful to remember that the most common type of two-conductor cord for low-power use in North America has smooth insulation on the "hot" side and ribbed insulation on the "neutral" side.