Test beam measurements at the test beam facilities of DESY have been conducted to characterise the performance of the EUDET-type beam telescopes originally developed within the EUDET project. The beam telescopes are equipped with six sensor planes using MIMOSA 26 monolithic active pixel devices. A programmable Trigger Logic Unit provides trigger logic and time stamp information on particle passage. Both data acquisition framework and offline reconstruction software packages are available. User devices are easily integrable into the data acquisition framework via predefined interfaces. The biased residual distribution is studied as a function of the beam energy, plane spacing and sensor threshold. Its standard deviation at the two centre pixel planes using all six planes for tracking in a 6 GeV electron/positron-beam is measured to be (2.88 ± 0.08) µm. Iterative track fits using the formalism of General Broken Lines are performed to estimate the intrinsic resolution of the individual pixel planes. The mean intrinsic resolution over the six sensors used is found to be (3.24 ± 0.09) µm. With a 5 GeV electron/positron beam, the track resolution halfway between the two inner pixel planes using an equidistant plane spacing of 20 mm is estimated to (1.83 ± 0.03) µm assuming the measured intrinsic resolution. Towards lower beam energies the track resolution deteriorates due to increasing multiple scattering. Threshold studies show an optimal working point of the MIMOSA 26 sensors at a sensor threshold of between five and six times their RMS noise. Measurements at different plane spacings are used to calibrate the amount of multiple scattering in the material traversed and allow for corrections to the predicted angular scattering for electron beams.