Measurements are presented from proton-proton collisions at centre-of-mass energies of root s = 0.9, 2.36 and 7 TeV recorded with the ATLAS detector at the LHC. Events were collected using a single-arm minimum-bias trigger. The charged-particle multiplicity, its dependence on transverse momentum and pseudorapidity and the relationship between the mean transverse momentum and charged-particle multiplicity are measured. Measurements in different regions of phase space are shown, providing diffraction-reduced measurements as well as more inclusive ones. The observed distributions are corrected to well-defined phase-space regions, using model-independent corrections. The results are compared to each other and to various Monte Carlo (MC) models, including a new AMBT1 pythia6 tune. In all the kinematic regions considered, the particle multiplicities are higher than predicted by the MC models. The central charged-particle multiplicity per event and unit of pseudorapidity, for tracks with p(T) > 100 MeV, is measured to be 3.483 +/- 0.009 (stat) +/- 0.106 (syst) at root s = 0.9 TeV and 5.630 +/- 0.003 (stat) +/- 0.169 (syst) at root s = 7 TeV.