Two basic designs have been developed for waveguide hybrids, or 3-dB couplers, capable of handling hundreds of megawatts at X-band. Coupling is provided by one or two connecting waveguides with h-plane junctions and matching elements. In the former case, the connecting waveguide supports two modes. Small apertures and field-enhancing e-bends are avoided to reduce the risk of RF breakdown. The h-plane symmetry also allows the use of over-moded rectangular waveguide in which the height has been increased to reduce field amplitudes without affecting the scattering matrix. The theory and designs are presented, along with the results of prototype tests of functionality and power-handling capability. Such a device is integral to the RF pulse compression or power distribution system of the Next Linear Collider (NLC) for combining, splitting, and directing power. This work was motivated by the observation of RF breakdown at power levels above 200 MW in conventional and modified magic-T's.