Spatial resolution is an important parameter for assessing the performance of positron emission tomography (PET) systems but this apparently simple measurement is complicated by various issues including the reconstruction algorithm, parameter settings and acquisition methodology. Here we describe a series of experiments that aim to untangle some of these issues. Measurements of PET spatial resolution were made using 3 different experimental arrangements: (1) a point source in air; (2) a point source in a radioactive background; and (3) a uniform cylinder positioned at a slightly oblique angle, allowing spatial resolution to be measured from the phantom edge response function. All experiments involved 18F and were performed on a clinical scanner, Biograph mCT. Ordered-subsets expectation maximization including time-of-flight (OSEM+TOF, no point spread function modelling) rapidly converged to a stable full-width at half-maximum (FWHM) for all 3 geometries. OSEM+TOF provided better spatial resolution than Fourier rebinning plus filtered back-projection (FORE+FBP). FWHM degraded with increasing radial distance but in a complex way, apparently dependent on the reconstruction algorithm. FWHM derived from point sources and OSEM+TOF were similar with or without a radioactive background (radial FWHM at 10 cm, 4.77 ± 0.11 mm vs. 4.78 ± 0.06 mm). A uniform cylinder positioned at an oblique angle allowed measurements of radial FWHM (4.74 ± 0.17 mm) that were very consistent with point source measurements. These results support use of the uniform cylinder phantom as a tool for resolution assessment that may be particularly useful for multi-center evaluations due to its simple set-up.