Summary: We carry out a thorough survey of entropy for a large class of \(p\)-branes in various dimensions. We find that the Bekenstein-Hawking entropy may be given a simple world volume interpretation only for the non-dilatonic \(p\)-branes, those with the dilaton constant throughout spacetime. The entropy of extremal non-dilatonic \(p\)-branes is non-vanishing only for solutions preserving 1/8 of the original supersymmetries. Upon toroidal compactification these reduce to dyonic black holes in 4 and 5 dimensions. For the self-dual string in 6 dimensions, which preserves 1/4 of the original supersymmetries, the near-extremal entropy is found to agree with a world sheet calculation, in support of the existing literature. The remaining 3 interesting cases preserve 1/2 of the original supersymmetries. These are the self-dual 3-brane in 10 dimensions, and the 2- and 5-branes in 11 dimensions. For all of them the scaling of the near-extremal Bekenstein-Hawking entropy with the Hawking temperature is in agreement with a statistical description in terms of free massless fields on the world volume.

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