Answer:
Yes, rabbits can get many different types of diseases. I will list several diseases below with a short explanation.
Weepy eye- Symptoms include inflamed eyes and discharged eyes. This can lead to a bacterial infection.
Coccidiosis- most common disease in rabbits and can be difficult to get rid of. It affects the intestinal functioning in the rabbit.
Caked mammary glands- milk not sufficiently removed from breast during pregnancy.
Ear Mites- External parasite that can cause itching, spasms, and sometimes nerve damage.

There are many more diseases that rabbits can get. This is just a few of the common ones. I suggest researching if you have a specific issue you need answers to.
First answer by Powell1991. Last edit by Powell1991. Contributor trust: 2 [recommend contributor recommended]. Question popularity: 0 [recommend question].