We report a measurement of the angular distributions of Drell-Yan dimuons produced using an 800 GeV/c proton beam on a hydrogen target. The polar and azimuthal angular distribution parameters have been extracted over the kinematic range 4.5<m micromicro<15 GeV/c2 (excluding the Upsilon resonance region), 0<p T <4 GeV/c, and 0<x F<0.8. The p+p angular distributions are similar to those of p+d, and both data sets are compared with models which attribute the cos2varphi distribution either to the presence of the transverse-momentum-dependent Boer-Mulders structure function h1 perpendicular to 1 or to QCD effects. The data indicate the need to include QCD effects before reliable information on the Boer-Mulders function can be extracted. The validity of the Lam-Tung relation in p+p Drell-Yan data is also tested.