Measurements of primary charged hadron multiplicity distributions are presented for non-single-diffractive events in proton-proton collisions at centre-of-mass energies of root s = 0.9, 2.36, and 7 TeV, in five pseudorapidity ranges from vertical bar eta vertical bar < 0.5 to vertical bar eta vertical bar < 2.4. The data were collected with the minimum-bias trigger of the CMS experiment during the LHC commissioning runs in 2009 and the 7 TeV run in 2010. The multiplicity distribution at root s - 0.9 TeV is in agreement with previous measurements. At higher energies the increase of the mean multiplicity with root s is underestimated by most event generators. The average transverse momentum as a function of the multiplicity is also presented. The measurement of higher-order moments of the multiplicity distribution con firms the violation of Koba-Nielsen-Olesen scaling that has been observed at lower energies.