Commercially available InGaAs/InP avalanche photodiodes, designed for optical receivers and range-finders, can be operated even biased above the breakdown voltage, achieving single-photon sensitivity. In this paper we describe in detail how to select the device for photon counting applications among commercial samples. Due to the high dark-counting rate the detector must be cooled below 100K and operated in gated mode. We have achieved Noise Equivalent Power of 3E-16W/HzE1/2 up to 1.55µm-wavelength and time resolution well below 1ns, with a best value of 200ps FWHM. Finally we compare these figures with the performance of state-of-the-art detectors in the near-infrared and we highlight the potentials of properly designed InGaAs/InP avalanch...