The two-nucleon density distributions in states with isospin T= 0, spin S= 1, and projection M S= 0 and±1 are studied in H 2, He 3, 4, Li 6, 7, and O 16. The equidensity surfaces for M S= 0 distributions are found to be toroidal in shape, while those of M S=±1 have dumbbell shapes at large density. The dumbbell shapes are generated by rotating tori. The toroidal shapes indicate that the tensor correlations have near maximal strength at r< 2 fm in all these nuclei. They provide new insights and simple explanations of the structure and electromagnetic form factors of the deuteron, the quasideuteron model, and the dp, dd, and αd L= 2 (D-wave) components in He 3, He 4, and Li 6. The toroidal distribution has a maximum-density diameter of∼ 1 fm and a half-maximum density thickness of∼ 0.9 fm. Many realistic models of nuclear forces predict these values, which are supported by the observed electromagnetic form factors of the deuteron, and also predicted by classical Skyrme effective Lagrangians, related to QCD in the limit of infinite colors. Due to the rather small size of this structure, it could have a revealing relation to certain aspects of QCD. Experiments to probe this structure and its effects in nuclei are suggested. Pair distribution functions in other T, S channels are also discussed; those in T, S= 1, 1 have anisotropies expected from one-pion-exchange interactions. The tensor correlations in T, S= 0, 1 states are found to deplete the number of T, S= 1, 0 pairs in nuclei and cause a reduction in nuclear binding energies via many-body effects.© 1996 The American Physical Society.