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We explore the role of inter-grain friction in determining the properties of non-spherical particle packings. We employ the Discrete Element Method (DEM) to generate sets of packings of different superellipsoidal grains over a range of inter-grain friction coefficients. We consider a broad range of grain shapes from spheres to ellipsoids and cuboids, and explore the full range of inter-grain friction values, from purely frictionless up to the infinite friction limit. Friction is demonstrated to play a key role in determining the mechanical properties of the system, determining the density of the loosest packings that can be realised, and strongly affecting the degree of ordering of the grains within the packing. By utilizing a range of order parameters, we are able to quantify how features of the individual grain shapes affect the properties of the system in the packed state. We find that anisotropy and broken rotational symmetry in the individual particle shapes play key roles in determining the properties of the resulting granular packings. [ABSTRACT FROM AUTHOR]