We investigate the manifestation of stripes in the in-plane resistivity anisotropy in untwinned single crystals of La2-xSrxCuO4 ( x = 0.02-0.04) and YBa(2)Cu(3)O(y) ( y = 6.35-7.0). It is found that both systems show strongly temperature-dependent in-plane anisotropy in the lightly hole-doped region and that the anisotropy in YBa(2)Cu(3)O(y) grows with decreasing y below approximately 6.60 despite the decreasing orthorhombicity, which gives most direct evidence that electrons self-organize into a macroscopically anisotropic state. The transport is found to be easier along the direction of the spin stripes already reported, demonstrating that the stripes are intrinsically conducting in cuprates.