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We present a general rule determining how extremal branes can interesect in a configuration with zero binding energy. The rule is derived in a model independent way and in arbitrary spacetime dimensions D by solving the equations of motion of gravity coupled to a dilaton and several different n-form field strengths. The intersection rules are all compatible with supersymmetry, although derived without using it. We then specialize to the branes occurring in type II string theories and in M-theory. We show that the intersection rules are consistent with the picture that open branes can have boundaries on some other branes. In particular, all the D-branes of dimension q, with 1 ≤ q ≤ 6, can have boundaries on the solitonic 5-brane.