From the NEJM:

We estimated that in 2008, breast cancer was over-diagnosed in more than 70,000 women; this accounted for 31% of all breast cancers diagnosed.

Data for U.S. women 40+:

Their conclusion:

Despite substantial increases in the number of cases of early-stage breast cancer detected, screening mammography has only marginally reduced the rate at which women present with advanced cancer. Although it is not certain which women have been affected, the imbalance suggests that there is substantial over-diagnosis, accounting for nearly a third of all newly diagnosed breast cancers, and that screening is having, at best, only a small effect on the rate of death from breast cancer.

HT: Kevin Outterson.