I cannot stress enough the importance of this first exam, you need to establish a relationship with a veterinarian. That way if the bunny is ever sick you have a veterinarian to make an appointment with. Veterinarians are busy; they will be more likely to squeeze in an emergency with an existing client over someone they don't know.

Rabbits are sensitive and because of that fact owners should be on the look out for signs of illness. Signs of illness in rabbits include but are not limited too:

Changes in behavior or Lethargy – If your pet rabbits behavior changes call your veterinarian for an appointment. If the bunny seems less active (lethargic) or doesn't want to play, doesn't want to leave it's bunny cage, etcetera, these are all reasons to contact the veterinarian.
Runny eyes or nose and sneezing – Runny eyes and/or nose and/or sneezing are signs of a respiratory infection.
Not eating – A rabbit that is off food and refusing treats could be ill.
Drooling – This is a symptom of a sore tooth. The rabbit might also be turning down crunchy food and treats.
Head tilt – Symptom of ear problems/infections.
Scratching/itching/shaking head – All symptoms of fleas and mites. These are a stubborn group and treatment needs to be begin immediately. Ask your veterinarian how to get rid of the fleas and/or mites. Rabbits are sensitive and the same products used on dogs and cats cannot be used on rabbits unless advised by a rabbit vet.
Lumps and abscesses – Rabbits are prone to abscesses so be on the look out for lumps on your rabbit. Antibiotics maybe necessary.
Stools – Watch your rabbit's stool for changes in color, size, dry/hard, or wet. These changes could indicate whether or not your rabbit has a healthy GI tract.
Urine – Also watch for changes in the rabbits urine. Bunny urine can be yellow to orange depending on what is being fed. If you question whether or not the urine is bloody have your vet test a sample – better safe than sorry. Bunny can get urinary tract infection, bladder stones, and cancer.
If your rabbit is displaying any of the above symptoms contact your rabbit veterinarian immediately. To truly know when your rabbit is sick you need to spend time with your pet. Play with your bunny and handle it (if tolerated) often. That is the only way you'll be able to catch illness early.

The information gathered for this article came from very interesting pet rabbit websites, so for more information and to give credit where credit is due I'll refer you back to them.

How to Recognize Illness in Your Rabbit

The two most noticeable signs of sickness in a rabbit are lethargy and feces that are smaller than normal, very soft, very dry or nonexistent. Get to know your rabbit well so that you will also notice any sudden changes in behavior.