The result of a search for heavy long-lived charged particles produced in pp collisions at sqrt(s) = 7 TeV at the LHC is described. The data sample has been collected using the CMS detector and corresponds to an integrated luminosity of 5.0 inverse femtobarns. The inner tracking detectors are used to define a sample of events containing tracks with high momentum and high ionization energy loss. A second sample of events with high-momentum and high-ionization tracks satisfying muon identification and long time-of-flight criteria is analyzed independently. In both cases, the results are consistent with the expected background estimated from data. The results are used to establish cross section limits as a function of mass within the context of models with long-lived gluinos, scalar top quarks and scalar taus. Cross section limits on hyper-meson particles, containing new elementary long-lived hyper-quarks predicted by a vector-like confinement model, are also presented. Lower limits at 95% confidence level on the mass of gluinos (scalar top quarks) are found to be 1098 (737) GeV. A limit of 928 (626) GeV is set for a gluino (scalar top quark) that hadronizes into a neutral bound state before reaching the muon detectors. The lower mass limit for a pair produced scalar tau is found to be 223 GeV. Mass limits for a hyper-kaon are placed at 484, 602, and 747 GeV for hyper-rho masses of 800, 1200, and 1600 GeV, respectively.