Grain morphology and crystallographic texture were investigated by electron microscopy in four different polycrystalline forms of superconducting MgB₂. The materials included a hot-pressed sintered MgB₂ pellet, a pellet reacted in situ from Mg and B, an in situ reacted MgB₂ filament and a pulsed-laser-deposited thin film grown on a single crystalline [111] oriented SrTiO₃ substrate. Thick plate-shaped grains with an aspect ratio of ~3 and large faces parallel to (0001) planes dominated the microstructure in all four types of sample. The intermediate-sized plate-shaped grains (0.1 μm × 0.3 μm on average) in the electromagnetically most homogeneous parts of the hot-pressed pellets were strongly facetted, but not textured. Large (3–5 μm) plate-shaped grains were seen in the pellet reacted directly from stoichiometric Mg and B. A tendency for parallel alignment of the [0001] axes of the considerably larger grains (~0.25 μm × 1 μm) in the filament was observed near its W core, but degradation of this texture away from the core was apparent. The very small grains (~10 nm) of the thin film possessed a well-defined fibre texture with [0001] parallel to the film normal and no preferred orientation in the plane of the film. Electrical resistivity of the finest grain samples was some 10³ times higher than the largest grain sample and their critical current density about one order of magnitude higher. We conclude that, in contrast to the cuprate-based high-T_c superconductors, grain boundaries do not limit the critical current density of polycrystalline MgB₂ and indeed act as flux-pinning centres, which enhance the critical current density.