Interactions of pairs of scroll waves in three-dimensional excitable media were studied experimentally in the Belousov-Zhabotinsky reaction by optical tomography. The behavior of two scroll waves depended on the distance d between their filaments. When the interfilament distance was shorter than the wavelength lambda of the scroll waves (but larger than the diameter of the spiral core), the filaments repelled each other. Once d approximate to lambda, the two scroll waves synchronized, rotating around their filaments with both a common rotation frequency and a common pitch. The interfilament distance of synchronized scroll waves did not change. When fluctuations broke the symmetry of the rotation periods, the scroll with higher rotation frequency displaced the slower rotating one, until the latter was ousted or even annihilated. These behaviors were independent of the sense of rotation (co- or counter-rotating), the filament dynamics (rigidly rotating or meandering tip motion in two-dimensional media), and the presence or absence of a gradient of excitability parallel to the filaments.