We present a purely hydrodynamic method for the high-throughput encapsulation of single cells into picoliter droplets, and spontaneous self-sorting of these droplets. Encapsulation uses a cell-triggered Rayleigh-Plateau instability in a flow-focusing geometry, and self-sorting puts to work two extra hydrodynamic mechanisms: lateral drift of deformable objects in a shear flow, and sterically driven dispersion in a compressional flow. Encapsulation and sorting are achieved on-flight in continuous flow at a rate up to 160 cells per second. The whole process is robust and cost-effective, involving no optical or electrical discrimination, active sorting, flow switching, or moving parts. Successful encapsulation and sorting of 70-80% of the injected cell population into drops containing one and only one cell, with <1% contamination by empty droplets, is demonstrated. The system is also applied to the direct encapsulation and sorting of cancerous lymphocytes from a whole blood mixture, yielding individually encapsulated cancer cells with a >10,000-fold enrichment as compared with the initial mix. The method can be implemented in simple "soft lithography" chips, allowing for easy downstream coupling with microfluidic cell biology or molecular biology protocols.