The purpose of this study is to test an innovative MRI breast cancer screening method in women with mammographically dense breasts as well as other women with moderately increased cancer risk. MRI, combined with other methods of risk assessment, has potential to significantly improve sensitivity to cancer in dense breasts and detect cancer in all cases at a much earlier stage, with far fewer interval cancers than mammography. Previous tests of MRI sensitivity show that this screening could significantly increase the likelihood of detecting invasive cancers resulting in decreased mortality from breast cancer. Suspicious lesions will be defined by the clinical interpretation of the breast MRI images performed by the attending breast radiologists. Based on the radiologist determination that the MRI findings are suspicious (these findings include masses, non-mass enhancement and foci), suspicious lesions will be assigned a Bi-Rads code specifying whether additional work up or biopsy is necessary. These are Bi-Rads codes 0, 4 and 5. False positive diagnosis should be minimized as all attending physicians reading breast MRI at this institution are fellowship trained in breast imaging.