Quite a lot has been written recently about rabbit's diets. I've updated this page to contain the most up to date information because this subject is so important.
It's also important to supplement the bunny's diet with timothy hay, and when you can find some, oat hay. Both are better than Alfalfa hay, which is too high in calcium. Oat and timothy hay are highly recommended by exotic animal vets who really know rabbits. Hay is about 33% fiber, and even modest eating on the rabbit's part helps the digestive tract a great deal. Also, avoid buying block hay that you see in pet stores. Rabbits typically don't like the block hay but will readily eat regular hay. Best to buy it from a local feed store that has fresh product available. Even here in the Los Angeles area, I have no trouble finding good hay.
Both hay and pellets need to be given fresh everyday, with unused portions being discarded. Think of eating a potato chip that has been sitting out in the open for two days. It would taste moist and yucky. That's what happens to pellets if left out too long. And remember, when switching pellets, do it gradually over a five day or so period to avoid upsetting the rabbits digestive system.
As one would imagine, rabbits love to eat vegetables. They will eat almost anything that grows from the ground. Unfortunately, being herbivores, they also love to eat most of my house plants and my palm trees in the backyard. As far as veggies go, the only ones I would avoid are cabbage (and cabbage related veggies) along with lettuce, celery and asparagus. Cabbage is too gassy and can hurt them while celery is too stringy. Lettuce has no nutritional value at all and asparagus must be too pungent for them. They don't seem to like it. Rabbits do love carrots and carrot tops, broccoli, brussel sprouts, cauliflower, spinach, bok choy, green peppers, radish tops, watercress, and cilantro. As stated in her article in "Rabbits" annual magazine, Dr. Linda Randall suggests a rabbit salad for your bunny that would contain "clover, peapods (not the peas), alfalfa sprouts in small amounts, dandelion greens, mustard greens, kale, carrot tops, parsley, collard greens and beet tops." These are all high in plant proteins, which she likes. As a treat, she recommends the following fruits; "apples, pears, peaches, papaya, pineapple and strawberries." She likes the fiber content of the these fruits. She goes on to say to avoid bananas and grapes, which are too high in sugar. She says to avoid starches that easily form sugars and are low in fiber, such as beans, peas, corn, wheat, barley and vegetables that grow under ground such as patatos, yams, turnips. She also says to avoid giving your rabbits breads, cereals, and pasta, which they will readily eat. Most small animal vets maintain that veggies should not dominate the diet, but should still be given every day. Most people do agree however, that one veggie shouldn't dominate the diet of the rabbit. In order to make sure that the bunny gets the best nutrition, a variety of the above veggies is the best thing to do. There are some elements of veggies that you don't want your bunny to overconsume. So variety is the best choice. However, when my male rabbit Harry was trying to get over pasturellosis, he stopped eating pellets, so I had to nurse him back to health on broccoli and apple slices. He fully recovered.
***It's also important to note that older rabbits may get diarrhea from veggies and fruits. I've had several emails from people with senior citizen aged rabbits that have had to stop giving veggie treats entirely. Many rabbit specialists will agree that older rabbits in particular need to stick to a very high fiber diet of pellets and hay only. Some high fiber veggies in small quantities may be okay, such as carrots. The best bet here with an older bunny is simply to stick with leafy green veggies, like bok choy, kale, and turnip and mustard greens.
Rabbits also need plenty of fresh water, made available to them 24 hours per day. The most important thing to remember is, keep it fresh. Water in a bottle or a crock needs to be replenished everyday. If you wouldn't drink the water, don't give it to them. As far as water crocks or food dishes go, make sure they are heavy enough so they won't be overturned. Rabbits love to stand on their food bowl with their front feet or play with it by turning it over. Many vets recommend cleaning the water bottle or crock everyday to insure that no bacteria or other harmful element infect the rabbit. Rabbits overall, prefer a nice heavy crock to drink from.