The properties of even-even O, Ca, Ni, Zr, Sn, and Pb isotopes from the beta-stability line to the neutron drip line are studied with the relativistic continuum Hartree-Bogoliubov theory, where both the spin-orbit interaction and continuum are properly taken into account. The available experimental binding energies E-b and two-neutron separation energies S-2n are reproduced very well. The predicted neutron drip-line nuclei are, respectively, Ca-74, Ni-100, Zr-140, Sn-176, and Pb-268. Based on the analysis of two-neutron separation energies, single-particle energy levels, the orbital occupation, the contribution of continuum and nucleon density distribution, giant halo phenomena due to pairing, correlation and the contribution from the continuum are suggested to appear in Ca isotopes with A>60 apart from Zr isotopes predicted earlier.