In this contribution we analyse the structural and optical properties of ZnO as well as ZnMgO nanopillars grown catalyst-free by metalorganic vapour-phase epitaxy. The nanostructures were grown directly onto different substrate materials with various orientations. The nanopillars deposited on a-plane sapphire show the best vertical c-axis alignment and have a typical diameter of about 50 nm and a height of several micrometres, depending on growth time. We achieved well ordered, almost completely c-axis oriented pillars, as confirmed by scanning electron microscopy and high resolution x-ray diffraction. Photoluminescence measurements revealed very narrow donor-bound exciton emission lines with half widths as small as 0.5 meV. In order to investigate the possibility of a combination of band gap engineering and nanopillar growth, ZnMgO nanopillars were also grown. The Mg incorporation was confirmed by photoluminescence measurements and a blue shift of the band gap of up to 170 meV could be achieved for the nanopillars with the highest Mg concentration.