An inclusive search is presented for new physics in events with two isolated leptons (electron or muon) having the same electric charge. The data are selected from events collected from pp collisions at sqrt(s) = 7 TeV by the ATLAS detector and correspond to an integrated luminosity of 34 inverse picobarns. The spectra in dilepton invariant mass, missing transverse momentum and jet multiplicity are presented and compared to Standard Model predictions. In this event sample, no evidence is found for contributions beyond those of the Standard Model. Limits are set on the cross-section in a fiducial region for new sources of same-sign high-mass dilepton events in the di-electron, di-muon and electron-muon channels. Four models predicting same-sign dilepton signals are constrained: two descriptions of Majorana neutrinos, a cascade topology similar to supersymmetry or universal extra dimensions, and fourth generation down-type quarks. Assuming a new physics scale of 1 TeV, Majorana neutrinos produced by an effective operator V with masses below 460 GeV are excluded at 95% confidence level. A lower limit of 290 GeV is set at 95% confidence level on the mass of fourth generation down type quarks. Show Partial Abstract