We describe mechanical metamaterials created by folding flat sheets in the tradition of origami, the art of paper folding, and study them in terms of their basic geometric and stiffness properties, as well as load bearing capability. A periodic Miura-ori pattern and a non-periodic Ron Resch pattern were studied. Unexceptional coexistence of positive and negative Poisson's ratio was reported for Miura-ori pattern, which are consistent with the interesting shear behavior and infinity bulk modulus of the same pattern. Unusually strong load bearing capability of the Ron Resch pattern was found and attributed to the unique way of folding. This work paves the way to the study of intriguing properties of origami structures as mechanical metamaterials.