Events with a final-state proton carrying a large fraction of the proton beam momentum, xL>0.6, and the square of the transverse momentum pT2<0.5 GeV2, have been studied in e+p collisions with the ZEUS detector at HERA. Data with different photon virtualities were used: Q2<0.02 GeV2, 0.1<Q2<0.74 GeV2 and 3<Q2<254 GeV2, corresponding to integrated luminosities of 0.9, 1.85 and 3.38 pb-1. The cross sections are given as a function of xL, pT2, Q2 and the Bjorken scaling variable, x. The ratio of the cross section for leading proton production to the inclusive e+p cross section shows only a mild dependence on Q2 and on x. In the region 0.6<xL<0.97, the relative yield of protons is only a weak function of xL.