Green building provides a lot of benefits for the homeowner. A green home will often be higher quality and more livable because of the intentional design. It should have cheaper (sometimes much cheaper) utility bills over the lifetime of the house. Residents should have a quality of life when they are not surrounded by materials that are leaking chemicals. For those who care about such things, living in a green home leaves you with the knowledge that your home construction resulted in less waste and likely used recyclable or renewable materials.
Some of this may come at a cost — wool carpet is more expensive. Low-VOC paint may cost more because it is less common. However, other choices, such as choosing bamboo flooring over exotic hardwoods or choosing local manufactured stone, may save money. Labor costs may be higher for new construction techniques, but money is saved when less material is wasted. High performance windows may cost more, but your energy costs are much lower over the lifetime of the home (plus, you will be less impacted if energy prices rise significantly).
Green building does not have to cost more; but in practice it is rare enough that we are still paying a premium due to the limited sources of green products and the limited number of workers trained in the proper building techniques. If nothing else, most green buildings probably have more time and effort put into design than a standard home, and that will increase costs. However, we think the cost will definitely be worth it for a better home in the end.