We describe the design and characterization of a fiber-coupled double-channel single-photon detection system based on superconducting single-photon detectors (SSPD), and its application for quantum optics experiments on semiconductor nanostructures. When operated at 2-K temperature, the system shows 10% quantum efficiency at 1.3-¿m wavelength with dark count rate below 10 counts per second and timing resolution <100 ps. The short recovery time and absence of afterpulsing leads to counting frequencies as high as 40 MHz. Moreover, the low dark count rate allows operation in continuous mode (without gating). These characteristics are very attractive-as compared to InGaAs avalanche photodiodes-for quantum optics experiments at telecommunication wavelengths. We demonstrate the use of the system in time-correlated fluorescence spectroscopy of quantum wells and in the measurement of the intensity correlation function of light emitted by semiconductor quantum dots at 1300 nm.