We have characterized the fundamental photoluminescence (PL) properties of individual, isolated indium phosphide (InP) nanowires to define their potential for optoelectronics. Polarization-sensitive measurements reveal a striking anisotropy in the PL intensity recorded parallel and perpendicular to the long axis of a nanowire. The order-of-magnitude polarization anisotropy was quantitatively explained in terms of the large dielectric contrast between these free-standing nanowires and surrounding environment, as opposed to quantum confinement effects. This intrinsic anisotropy was used to create polarization-sensitive nanoscale photodetectors that may prove useful in integrated photonic circuits, optical switches and interconnects, near-field imaging, and high-resolution detectors.