In Einstein's gravity, the entropy of horizons is proportional to their area. Several arguments given in the literature suggest that, in this context, both area and entropy should be quantized with an equally-spaced spectrum for large quantum numbers. But in more general theories (like, for example, in the black hole solutions of Gauss-Bonnet or Lanczos-Lovelock gravity) the horizon entropy is not proportional to area and the question arises as to which of the two (if at all) will have this property. We give a general argument that in all Lanczos-Lovelock theories of gravity, it is the entropy that has an equally-spaced spectrum. In the case of Gauss-Bonnet gravity, we use the asymptotic form of quasinormal mode frequencies to explicitly demonstrate this result. Hence, the concept of a quantum of area in Einstein-Hilbert gravity needs to be replaced by a concept of quantum of entropy in a more general context. © 2008 The American Physical Society.