Our pet rabbits' hutch is always open. so they run free over half the garden and the large patio area. Besides their usual pelleted food, they have loads of grass to eat, are given bundles of fresh hay every day, along with cabbages and the odd carrot, but they still choose to eat everything else in the garden - yes, even those things that apparently they don't like.
Sometimes I ask for trouble, though, as I forget about the rabbits and do something rash like bring some plants back from the garden centre and leave them on the patio for a few minutes whilst I rummage in the potting shed, only to come back out and find there's no plants left! I lost lots of fuchsias that way last year. They do love their fuchsias - and bulbs, especially crocus, although they're not too keen on daffodils.
I know it's our fault for letting them have their freedom in the first place, but we didn't want to keep them caged and they really are VERY happy, running around and playing (and nibbling my plants!). It helps that they are incredibly cute as well, especially when they sit up and wash their ears which makes them just look like Thumper from Bambi. I love my garden as well, though, so I'm going to have to have a re-think. I don't think the answer is rabbit stew though!