Charged-particle pseudorapidity densities are presented for the d + Au reaction at sqrt[s(NN)] = 200 GeV with -4.2 < or = eta < or = 4.2. The results, from the BRAHMS experiment at BNL Relativistic Heavy-Ion Collider, are shown for minimum-bias events and 0%-30%, 30%-60%, and 60%-80% centrality classes. Models incorporating both soft physics and hard, perturbative QCD-based scattering physics agree well with the experimental results. The data do not support predictions based on strong-coupling, semiclassical QCD. In the deuteron-fragmentation region the central 200 GeV data show behavior similar to full-overlap d+Au results at sqrt[s(NN)] = 19.4 GeV.