We present a method for ultrafast automated single-cell optical microscopy that performs blur-free image acquisition and non-stop real-time image-recording and classification of cells during high-speed flow. This method is based on a unique integration of ultrafast optical imaging, self-focusing microfluidics, optoelectronics, and information technology. To show the system's utility, we demonstrate high-throughput image-based screening of rare breast cancer cells in blood with an unprecedented throughput of 100,000 cells/s and a record false positive rate of one in a million. This method is expected to be effective for early, noninvasive, low-cost detection of cancer.