We consider the wave equation damped by a nonlinear boundary velocity feedback q(u(t)). First we consider the case where q has a linear growth at infinity. We prove that the usual decay rate estimates proved by Nakao [Differential Integral Equations, 8 (1995), pp. 681-688], Haraux and Zuazua [Arch. Rational Mech. Anal., 100 (1988), pp. 191-206], Conrad, Leblond, and Marmorat [in Proceedings of the Fifth International Federation of Automatic Control Symposium on Control of Distributed Parameter Systems, Perpignan, 1989, pp. 101-116], Zuazua [SIAM J. Control Optim., 28 (1990), pp. 466-477], and Komornik [in Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena, Internat. Ser. Numer. Math. 118, Birkhauser, Basel, 1994, pp. 253-266] when q has a polynomial behavior at zero and by the second author [ESAIM Control Optim. Calc. Var., 4 (1999), pp. 419-444] in the general case are in fact optimal in one space dimension. More generally, we prove that the energy decays exactly like the solution of an explicit and simple ordinary differential equation. Next we study the problem when q is bounded at infinity. We prove that strong solutions decay exponentially to zero, and we exhibit a sequence of weak solutions for which the associated energy decays to zero at infinity as slowly as the iterated logarithms go to infinity at infinity.