Rabbits might enjoy eating all kinds of vegetables, but the healthiest vegetables for them to eat are leafy greens and green herbs. This includes lettuce, cabbage, kale, basil, parsely, collard greens, endive, and carrot greens. Root vegetables, such as carrots, make a nice treat but shouldn't be offered too often due to their high sugar content. Offer new greens gradually because too much at once could cause a stomach upset.;