We report, for the first time to our knowledge, observation of polarization bistability from 1.55-${mu}m$ wavelength single-mode VCSELs of a conventional cylinder-shape under control of their driving current, and demonstration of all-optical flip-flop (AOFF) operations based on the bistability with optical set and reset pulse injection at a 50 MHz switching frequency. The injection pulse energy was less than 14 fJ. The average on-off contrast ratio of the flip-flopped signals was about 7 dB. These properties of the VCSELs will be potentially useful for future high-speed all-optical signal processing applications.