Oral contraceptives actually reduce the risk of ovarian and endometrial cancers. Ovarian cancer is particularly deadly because is it usually diagnosed only after it’s quite advanced. The evidence for oral contraceptive use increasing breast cancer risk is still pretty weak — most of the statistical difference seen is probably attributable to delayed childbearing rather than oral contraceptive use (i.e. women who would have gotten cancer anyway, even if they’d been relying on condoms or diaphragms or IUDs).
It is now well established that birth control medications (contraceptive steroids) increase breast cancer risk, especially if they are taken before the first full-term pregnancy, when breast cells are still immature. Birth control pills are very commonly used by young women. In one study, women who took birth control pills before the age of 20 had a more than ten-fold increased risk of breast cancer. The longer the pill is used, the higher the risk. Contraceptive steroids increase risk whether they are given orally (i.e., "the pill"), by injection (e.g., Depo_provera), implantation, through the skin with a patch, intravaginally with a ring (e.g., Nuva Ring) or with an intrauterine device (IUD). Even "low dose" estrogen pills have been associated with higher breast cancer risk.