Solar Powered Lawn Mowers
Whether you do it your self or buy on these are a great option. Not only are they relatively quite compared to their petrol powered counterparts, they also are environmentally friendly which means your not breathing in those fumes as you are cutting your lawn.
Bought ones
The best of the bought ones not only are quite and green but are robotic so the mower the lawn for you. Husqvarna is currently trialing a new solar robotic lawn mower to hit the markets soon (*est. $US2,500).
Homemade ones
The most popular instructions on home to do this yourself are at pequals and appropedia. This walks you through from scratch on how to rip apart an old lawn mower, attach an electric motor and battery and charge it from a solar panel. This is a great project that most people can handle.
Of course you can extend the idea of this, browse around for an electric lawn mower that uses less power than the average one and strap some batteries to it and charge them from some panels.
Not solar but still green
How about a biodiesel one? About biodiesel mowers.
The greenest and cheapest are still are the traditional push mowers. Quite and produce no emissions (unless you have been on the beans the night before). Keep them in mind if your looking down the green path.