We study the capacity of Nakagami multipath fading (NMF) channels with an average power constraint for three power and rate adaptation policies. We obtain closed-form solutions for NMF channel capacity (with and without diversity) for each power and rate adaptation strategy, and compare them with the additive white Gaussian noise (AWGN) channel capacity. The capacity of a NMF channel is always smaller than the capacity of an AWGN channel. Moreover, the capacities converge to the AWGN channel capacity as the Nakagami fading parameter m tends to infinity, as expected. Our results also show that optimal power and rate adaptation yields a small increase in capacity over just optimal rate adaptation with constant power, and this small increase in capacity diminishes as the average received carrier-to-noise ratio, m parameter, and/or number of diversity branches increase. Finally, fixed rate transmission with channel inversion suffers the largest capacity penalty. However, this penalty diminishes as the amount of fading decreases.