Anything. They eat ANYTHING. If they don't want to eat it, they will scratch it up to eat whatever is under it.
My chickens are allowed to roam in our large yard a lot, and we also have a lot of landscaping and flower beds. We cover all or our newly planted areas with bird mesh and surround them with hogwire. It works pretty well, but they still find ways in. They're mainly only allowed to free range completely while I am home to moniter. It takes a lot of effort and creativity, but it IS possible to have landscaping and chickens.
If you don't want to spend the time chicken-proofing your landscaping, I would suggest little playthings in the coop. My girls have a wild birdfeeder that acts like a time released capsule that they have to rotate and peck while its swinging in order to get the treats out. I also hang cabbage (lettuce, broccoli, etc) on a chain attached to a screw. I call it cabbage tetherball. They love it and it keeps them entertained, as well as saving your plants.