Single-photon detectors (SPDs) at near infrared wavelengths with high system detection efficiency (> 90%), low dark count rate (< 1 counts per second, cps), low timing jitter (< 100 ps), and short reset time (< 100 ns) would enable landmark experiments in a variety of fields. Although some of the existing approaches to single-photon detection fulfill one or two of the above specifications, to date no detector has met all of the specifications simultaneously. Here we report on a fiber-coupled single-photon-detection system employing superconducting nanowire single photon detectors (SNSPDs) that closely approaches the ideal performance of SPDs. Our detector system has a system detection efficiency (SDE), including optical coupling losses, greater than 90% in the wavelength range lambda = 1520-1610 nm; device dark count rate (measured with the device shielded from room-temperature blackbody radiation) of ~ 0.01 cps; timing jitter of ~ 150 ps FWHM; and reset time of 40 ns.