Vertically aligned single-crystal ZnO nanorods have been successfully fabricated on semiconducting GaN, Al0.5Ga0.5N, and AlN substrates through a vapor-liquid-solid process. Near-perfect alignment was observed for all substrates without lateral growth. Room-temperature photoluminescence measurements revealed a strong luminescence peak at approximately 378 nm. This work demonstrates the possibility of growing heterojunction arrays of ZnO nanorods on AlxGa1-xN, which has a tunable band gap from 3.44 to 6.20 eV by changing the Al composition from 0 to 1, and opens a new channel for building vertically aligned heterojunction device arrays with tunable optical properties and the realization of a new class of nanoheterojunction devices.