Through experiments and simulations, the consequences of symmetry on the coherent backscattering enhancement (CBE) are studied in cavities. Three main results are highlighted. First, the CBE outside the source is observed (a) on a single symmetric point in a onedimensional (1-D) cavity, in a disc and a symmetric chaotic plate, (b) on three symmetric points in a 2-D rectangle, and (c) on seven symmetric points in a 3-D parallelepiped cavity. Secondly, the existence of enhanced intensity lines and planes in 2-D and 3-D simply-shaped cavities is demonstrated. Thirdly, we show how the anti-symmetry caused by special boundary conditions is responsible for the existence of a coherent backscattering decrement with a dimensional dependence of 3/2^d with d =1,2,3 as the dimensionality of the cavity.