We theoretically study discrete Talbot self-imaging in hexagonal, square, and irregular two-dimensional waveguide arrays. Different from its counterpart in a continuous system, the periods of the input fields must belong to {1, 2, 3, 4, 6} for Talbot self-imaging. Also, the combinations of the input periods cannot be 3 & 4, or 4 & 6 along two different directions, which distinguishes itself from the one-dimensional discrete Talbot effect.