The influence of the positron distance of flight in various human tissues on the spatial resolution in positron emission tomography (PET) was assessed for positrons from carbon-11, nitrogen-13, oxygen-15, fluorine-18, gallium-68 and rubidium-82. The investigation was performed using the Monte Carlo code PENELOPE to simulate the transport of positrons within human compact bone, adipose, soft and lung tissue. The simulations yielded 3D distributions of annihilation origins that were projected on the image plane in order to assess their impact on PET spatial resolution. The distributions obtained were cusp-shaped with long tails rather than Gaussian shaped, thus making conventional full width at half maximum (FWHM) measures uncertain. The full width at 20% of the maximum amplitude (FW20M) of the annihilation distributions yielded more appropriate values for root mean square addition of spatial resolution loss components. Large differences in spatial resolution losses due to the positron flight in various human tissues were found for the selected radionuclides. The contribution to image blur was found to be up to three times larger in lung tissue than in soft tissue or fat and five times larger than in bone tissue. For (18)F, the spatial resolution losses were 0.54 mm in soft tissue and 1.52 mm in lung tissue, compared with 4.10 and 10.5 mm, respectively, for (82)Rb. With lung tissue as a possible exception, the image blur due to the positron flight in all human tissues has a minor impact as long as PET cameras with a spatial resolution of 5-7 mm are used in combination with (18)F-labelled radiopharmaceuticals. However, when ultra-high spatial resolution PET cameras, with 3-4 mm spatial resolution, are applied, especially in combination with other radionuclides, the positron flight may enter as a limiting factor for the total PET spatial resolution--particularly in lung tissue.