Broccoli and other similar vegetables are not good for rabbits. Although some people feed these items to their rabbits, letting them eat too much of it can cause gas and bloating. This is because the natural diet of rabbits is primarily hay and not vegetables. Bacteria in the gut of the rabbit work to ferment fiber to produce energy, B-vitamins, and other nutrients that the rabbit can use. Broccoli and other vegetables are fermented too quickly and can shift the population of bacteria and change the pH. Digestive upset like this can lead to diarrhea and death. Any veggies that are fed to rabbits but should only be given in very small amounts as a treat.
Rabbits will be far healthier when fed a balanced diet specially designed for them. Adult rabbits should be fed a grain & soy-free low-energy maintenance type rabbit food that is rich in fiber like timothy hay. It is important to fortify this diet with specific vitamins and minerals to ensure long-term health. This diet will also keep them healthy, trim, and playful. Baby rabbits require a high-fat diet like "mamma's milk" that also provided quality balanced protein (not soy!). Rabbit food too rich in grains and grain by-products can cause diarrhea and should be avoided.
So, don't feed too much broccoli to rabbits because they can't handle eating it!