Name badges should be worn on the right side of a shirt. Since most people shake hands with their right hand when they greet someone, their right side is more prominent, making the name tag easier to read.
Although it is easier for most right-handed people to put a name tag on their left side, it is worth the slight difficulty to pin it on the right side instead. The name tag should be placed above any pocket on the jacket or shirt. Women's name tags should be placed closer to the shoulder than to the breast to avoid any awkwardness if someone needs to lean close to read the name.