Although it is quite rare, a large cysts can become twisted, this is called ovarian torsion. This can cause severe abdominal pain, nausea, and vomiting. If it is not treated the ovary can be deprived of its blood supply, causing ovarian failure.
It is also possible for the cysts to rupture (burst). A ruptured cyst can be very painful and dangerous, especially if it is filled with blood.