We have a wood fenced backyard. This means there is a 1-2" gap underneath the fence, to keep the dirt from advancing the decomposing of the lumber. Rabbits come sliding under the fence no problem, eating all of our plants, and leaving their droppings behind.
I have gotten sick and tired of the rabbits in our backyard, so I dug a trench (about 8" deep) under my fence, for the entire stretch around my yard (about 250'). Then took this wire and laid it in the trench, attaching one side to bottom board of my fence with a staple gun. Then I filled the dirt back in over top of the fence wire.
This has proven to be an impenetrable fence, and we haven't had a rabbit in our yard for months. It was a bit of work, but at least my flowers are blooming, and our plants have leaves on them.