Self-collimation is a dispersion property of many photonic crystals (PCs), in which light beam can propagate free of divergence in the PCs. While self-collimation is a desired property for applications related to wave guiding and light collection, most of the current self-collimating PCs have restrictions on incident angles and/or operating wavelengths. These restrictions limit the operation flexibility of current self-collimating devices, and prevent the usefulness of self-collimation in many potential applications. In this dissertation, different PC structures are proposed to enable broadband, (in-plane) "all-angle" self-collimation or three-dimensional (3D) "omnidirectional" self-collimation. For in-plane self-collimation, a group of non-conventional two-dimensional (2D) PC structures inspired by the irradiance distributions resulting from the fractional Talbot effect ("Talbot crystals") is studied for the first time. A complex rhombus lattice Talbot crystal is found to support broadband virtual "all-angle" self-collimation. Such concepts are further extended to 3D. Multiple PC structures and different design strategies are proposed and compared in terms of the resulting self-collimation performance. Several desired 3D properties are realized for the first time, including broadband virtual 3D limited-angled self-collimation, 3D omnidirectional beam confinement, and broadband 3D omnidirectional self-collimation. These results may enable future self-collimation applications, such as PC core fibers and solar light collection, and suggest a possible whole-band self-collimation phenomenon.