The structural and optical properties of the ZnO, Al-doped ZnO, Ga-doped ZnO, and In-doped ZnO nanorods were investigated using field-emission scanning electron microscopy, X-ray diffraction, photoluminescence (PL) and ultraviolet-visible spectroscopy. All the nanorods grew with good alignment on the ZnO seed layers and the ZnO nanorod dimensions could be controlled by the addition of the various dopants. For instance, the diameter of the nanorods decreased with increasing atomic number of the dopants. The ratio between the near-band-edge emission (NBE) and the deep-level emission (DLE) intensities ($I_{NBE}/I_{DLE}$) obtained by PL gradually decreased because the DLE intensity from the nanorods gradually increased with increase in the atomic number of the dopants. We found that the dopants affected the structural and optical properties of the ZnO nanorods including their dimensions, lattice constants, residual stresses, bond lengths, PL properties, transmittance values, optical band gaps, and Urbach energies.