We evaluate the performance of various commercially available InGaAs/InP avalanche photodiodes for photon counting in the infrared at temperatures that can be reached by Peltier cooling. We find that dark count rates are high, and this can partially saturate devices before optimum performance is achieved. At low temperatures the dark count rate rises because of a strong contribution from correlated afterpulses. We discuss ways of suppressing these afterpulses for different photon-counting applications.