We report on synthetic strategies to fabricate DNA-coated micrometer-sized colloids that, upon thermal annealing, self-assemble into various crystal structures. Colloids of a wide range of chemical compositions, including poly(styrene), poly(methyl methacrylate), titania, silica, and a silica-methacrylate hybrid material, are fabricated with smooth particle surfaces and a dense layer of surface functional anchors. Single-stranded oligonucleotides with a short sticky end are covalently grafted onto particle surfaces employing a strain-promoted alkyne-azide cycloaddition reaction resulting in DNA coatings with areal densities an order of magnitude higher than previously reported. Our approach allows the DNA-coated colloids not only to aggregate upon cooling but also to anneal and rearrange while still bound together, leading to the formation of colloidal crystal compounds when particles of different sizes or different materials are combined.