We describe a versatile microfluidic fluorescence-activated cell sorter that uses acoustic actuation to sort cells or drops at ultra-high rates. Our acoustic sorter combines the advantages of traditional fluorescence-activated cell (FACS) and droplet sorting (FADS) and is applicable for a multitude of objects. We sort aqueous droplets, at rates as high as several kHz, into two or even more outlet channels. We can also sort cells directly from the medium without prior encapsulation into drops; we demonstrate this by sorting fluorescently labeled mouse melanoma cells in a single phase fluid. Our acoustic microfluidic FACS is compatible with standard cell sorting cytometers, yet, at the same time, enables a rich variety of more sophisticated applications.