The settling velocities of 66 microplastic particle groups, having both regular (58) and irregular (eight) shapes, are measured experimentally. Regular shapes considered include: spheres, cylinders, disks, square plates, cubes, other cuboids (square and rectangular prisms), tetrahedrons, and fibers. The experiments generally consider Reynolds numbers greater than 10², extending the predominant range covered by previous studies. The present data is combined with an extensive data set from the literature, and the settling velocities are systematically analyzed on a shape-by-shape basis. Novel parameterizations and predictive drag coefficient formulations are developed for both regular and irregular particle shapes, properly accounting for preferential settling orientation. These are shown to be more accurate than the best existing predictive formulation from the literature. The developed method for predicting the settling velocity of irregularly-shaped microplastic particles is demonstrated to be equally well suited for natural sediments in the Appendix.