Most of the time, pet rabbits are very clean animals, and great pets for those with children. There are very few health risks associated with having them as pets. However, there are some that you need to be aware of, just to monitor signs. Even though there are a few health risks to people owning rabbits, you need to know that they are very rare, and there is little to worry about with owning one. Tetanus is the most dangerous possible disease that you could get from rabbit scratches or bites. Providing you have had all of your immunizations, though, it is extremely unlikely that you will be affected.
Other possibilities, such as E. Cuniculi (a parasite), Ringworm (fungal infection), Pasteurella (bacteria), and Cheyletiella (fur mites), are all theoretical problems that you may face as a rabbit owner. However, they are unlikely to cause any issues to healthy people. One thing that you need to know, though, is that those people with weakened immune systems are at higher risk of complications. Therefore, it is advised that they do not own them.