There are so many reasons to dry clothing on a clothesline. The smell is reminscent of everything summer and wonderful. The image is charming and quaint.
Beyond that, the obvious benefit is electric conservation. Additionally, an opportunity to extend the life of your clothes. The lint in a dryer is the clothing fibers breaking down. Another benefit is that clothing dried on a line rarely needs ironing, it dries flat and wrinkle free.
For some, there are homeowner's restrictions or stigmas. This can be circumvented with a very clever garage clothesline, to dry your clothes in the privacy of your own garage. In the winter, hanging racks are also available, which also will help humidify your air, cutting down on static electricity.
Living green involves a lot of lifestyle changes, I suggest incorporating them little by little, such as trying to dry at least one load a week on a line, until it becomes second nature. Your electric company may not send you any thank you notes, but your wallet will.