Remember this cool artist with the hidden handguns? When I was looking through the archive of her stuff I came across this cool chart of the cost of mowing a lawn.
As you can see, the sheep is the most cost effective method for keeping a trimmed lawn. You would have to watch out for little sheepie poopies, though. And there might be some issues with zoning ordinances and home owner associations.
Be sure to look at the other things she has made by clicking here. You won't regret it.