Erect a chicken wire fence around the entire garden. A chicken wire fence that encases the entire vegetable garden is probably the most effective, yet labour-intensive way to prevent rabbits from munching the garden down to bare stems. When erecting the fence, remember that rabbits are diggers, so the chicken wire must penetrate the soil level about eight inches deep.

Fencing. If rabbits are the only varmints causing problems in your vegetable garden, a simple 2 ft.-high fence made of poultry mesh will usually solve the problem. Make sure the mesh has 1″ diameter or smaller (3/4″ is safer) and that you secure it to sturdy stakes. The fence needs to extend into the soil to discourage burrowing — 6″ if you can. This means that if you want a 2 ft. fence, you'll need to purchase 3 ft. fencing. If your problem is jackrabbits, rather than garden variety cottontails, or if your cottontails are particularly athletic, you can make the fence a little taller. For added protection, bend the top 5-6″ to deter jumping (top edge faces away from the garden).

Plastic fencing is another option. Follow the same installation instructions as above. Plastic fencing can be easily cut to size, and if you wish, can be removed at season's end and re-used the following year.

If your garden is already surrounded by a picket fence and rabbits are still getting in, add a 2-3 ft. band of chicken wire to the bottom of the fence, making sure to bury at least 6″ of it below ground to prevent burrowing.

It worked for me. I had a lot of rabbits and deer coming in my garden. I also surround a single plant with wire mesh if I have to. Good luck!

Thanks Michaella.

http://www.which.co.uk/documents/pdf/rabbits-153694.pdf has an excellent article on deterring rabbits by using netting wire with an extended bit at the bottom going away from the fence at an angle under the soil or just laid on top and pegged down. It works we have used it in the past.

Thanks scotsgran.