Highly sensitive photodetectors with single photon level detection is one of the key components to a range of emerging technologies, in particular the ever-growing field of optical communication, remote sensing, and quantum computing. Currently, most of the single-photon detection technologies require external biasing at high voltages and/or cooling to low temperatures, posing great limitations for wider applications. Here, we demonstrate InP nanowire array photodetectors that can achieve single-photon level light detection at room temperature without an external bias. We use top-down etched, heavily doped p-type InP nanowires and n-type AZO/ZnO carrier selective contact to form a radial p-n junction with a built-in electric field exceeding 3x10^5 V/cm at 0 V. The device exhibits broadband light sensitivity and can distinguish a single photon per pulse from the dark noise at 0 V, enabled by its design to realize near-ideal broadband absorption, extremely low dark current, and highly efficient charge carrier separation. Meanwhile, the bandwidth of the device reaches above 600 MHz with a timing jitter of 538 ps. The proposed device design provides a new pathway towards low-cost, high-sensitivity, self-powered photodetectors for numerous future applications.