This study will evaluate women who are at increased genetic risk of developing ovarian cancer because they or a close relative have a mutation in the BRCA1 or BRCA2 gene (the genes that cause most of the genetic forms of ovarian cancer) or because they have a very strong family history of breast and/or ovarian cancer. The study has two aspects. There will be two groups of subjects in this study. One group of women who will have their ovaries and fallopian tubes surgically removed as a prophylactic (preventive) measure against developing ovarian/fallopian tube cancer. These women will be studied to determine whether the surgery does, in fact, decrease the risk of ovarian or tubal cancer and whether it decreases the risk of breast and other cancers. The tissue removed at surgery will also be investigated to see whether a new way of examining the ovaries after they are removed provides better information about cancer-related tissue changes. A second group of subjects will be women who choose not to have preventive surgery. These women will be followed closely to see if screening with multiple CA-125 blood testing over time (see below) can detect ovarian or tubal cancers in their early stages. Both groups of women will undergo examination of the process by which women decide upon various options for lowering their ovarian cancer risk and a detailed assessment of how their choice impacts their quality of life. It will look at how those who opt for ovariectomy feel after their surgery and how those who choose screening feel during the time of screening.