It's not a roofing solution so much as an alternative building type, but you could also build a monolithic dome. It needs no roofing at all since its walls and roof are the same monolithic structure. No roofing material and minimal maintenance make it a winner beyond its energy efficiency and disaster resistance. If you paint it white it will also reflect light in the way mentioned above.

A green roof could be as simple as a roof that is built with the sun's movement though the sky in mind, with eve depths, wall placement, and angles and placement of everything designed to let in more light during the winter and keep the windows in the shade of the eves during the heat of summer. A passive heating/cooling system designed in to the roof can do much to making a house much more efficient.

Before fretting about shelling out tens of thousands for a photovoltaic roof, consider a solar water heater first; solar water heaters pre-heat water and store the water, reducing the amount of fuel that needs to be burnt to heat it the rest of the way, if that is even necessary; much of the hot water we use for showering and bathing gets diluted with cold water to cool it down to a comfortable temperature to begin with. Showering with straight-up solar heated water would eliminate that need. On a per-dollar basis, solar water heaters are a better investment than photovoltaic panels.

In my heirarchy of spending, I'd rank solar roofs this way:
1) angles and directions and air gaps calculated to passively warm and cool the house.
1.5) sky lights and solar light tubes. (lighting wastes so much electricity, wiring, and other resources. Just use the sun!)
2) solar water heater
3) photo voltaic panels

I've built a monolithic dome. It does address some roofing issues, but has some huge environmental issues as well. The dome's exterior is largely made up of a thick vinyl-like material. The material was actually inflated in place with a gigantic fan. Then a stiff foam material is sprayed on it. It is a mix of two materials that form the foam as they are mixed together with air and shot out with compressed air. The applicators can barely breathe even with expensive respirators while they apply this on the interior of the dome, mostly while standing on a lift. The foam holds reinforcing bar in place after a second application and concrete is compressed and shot onto the surfaces of the dome interior in multiple applications.
No doubt this is a strong structure that even withstood a bunker buster bomb in Iraq. The insulating qualities are phenomenal and can reduce long-term costs, but at quite an environmental first cost. Unfortunately, the aesthetics of the dome are only decent on the interior and downright poor on the exterior. As the vinyl exterior gets worn over the years, it presents unique structural and environmental issues as you consider how to paint on vinyl in an exterior application or recover the dome with more vinyl.
There are other types of monolithic domes out there utilizing other exterior and insulating materials, but long term something unique like a dome doesn't address many of our core environmental challenges in roofing.
As an architect and general contractor we are often challenged by how we might clean up our industry both environmentally and in other areas. Roofing is a huge challenge. It represents most of the rework and legal issues stemming from construction quality related problems.
A green roof is a fabulous idea in some regards. In an urban area building exceeding 10 stories it is not a large issue to add this functional aesthetic. However it is actually exceedingly harmful for the environment within single family structures and low-rise structures under 10 stories or so. This is because of the additional weight of adding something of this nature to the structure.
First, there is really a roof built under the green roof to keep out the water - so essentially you're building a garden over the asphalt. Now you are working against your roof - keeping moisture out - by keeping moisture in, only inches above it! Then the structure must be strengthened to accomodate the extra weight of the water, dirt and vegetation. Even given special lightweight soils, the water weight alone adds up in a hurry! A roof is usually constructed for the minimal weight it must hold. Usually this just means the shingles and the snowload. (In a factory with overhead cranes or in site conditions requiring rooftop units for the HVAC the structure has been further strengthened.) This means more steel, more wood, more concrete in the foundations, more fuel to bring the additional material to the site, more fuel to manufacture the materials, more fuel to get more workers to work to create the materials, more fuel to bring the raw materials from asia, more fuel to mine the raw materials, etc.
A roof is inherently under attack from nature. Sun, water, foreign organic materials, etc. Roofs are almost inherently unnatural, but one of our greatest human needs. Environmentally we will always have some type of net negative affect on nature when we create long-term shelters to cover the spaces where we live and work. We are left looking for the best of the negative choices. Looking for a net even or positive affect on nature while addressing a roof on a permanent facility is a challenge that will never be realized without the willingness to embrace a wildly unusual and unique lifestyle within organic or cavelike conditions...not exactly practical for the urban settings we find ourselves in today.