We have investigated magnetic and transport properties of 5% Co-doped and undoped ZnO thin films deposited on $r$ plane ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ substrates by pulsed laser deposition. The Co doped films showed paramagnetic and ferromagnetic behavior as well as a high magnetoresistance and a small anomalous Hall effect. In a range of $0\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}5\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ at low temperatures we observed a double sign change of the magnetoresistance. For undoped ZnO films, prepared by the same conditions, only a negative MR was observed, but surprisingly also a very small anomalous Hall effect. We explain our results by applying a semiempirical fit consisting of a positive and a negative contribution to the magnetoresistance. Using x-ray magnetic circular dichroism we investigated element specific magnetic moments in Co-doped laser ablated ZnO films. As the Co atoms show a paramagnetic behavior, we attribute the ferromagnetism to a spontaneously spin impurity band induced by oxygen vacancies and defects due to the transition metal doping and/or interface stress to the substrate.