Researchers will use the pattern and rate of change of CA-125 levels over time in women in the screening group to decide if more tests are needed to test for ovarian cancer. Women in the surgery portion will undergo surgical removal of their ovaries and fallopian tubes. The removed tissues will be studied using new methods to examine the cells more closely than usual, and a portion of the tissues will be stored for future research on ovarian cancer. This study is being conducted in collaboration with the Gynecologic Oncology Group (GOG), and is designated GOG Protocol 0199. Subjects may join the study at any participating GOG institution (http://www.gog.org).