A new intuitive method for the rapid calculation of the nonanalytic behavior of hadronic observables in standard, quenched and partially-quenched chiral perturbation theory is presented. After proving the technique in a consideration of octet baryon masses, the quark-flavor contributions to the magnetic moments of octet baryons are calculated in full, quenched and partially-quenched QCD. The technique provides a separation of quark-sector magnetic-moment contributions into direct sea-quark loop, valence-quark, indirect sea-quark loop and quenched valence contributions, the latter being the conventional view of the quenched approximation. Both meson and baryon mass violations of SU(3)-flavor symmetry are accounted for. A comprehensive examination of the individual quark-sector contributions to octet baryon magnetic moments reveals numerous exciting opportunities to observe and understand the underlying structure of baryons and the nature of chiral nonanalytic behavior in QCD and its quenched variants. In particular, the valence u-quark contribution to the proton magnetic moment provides the optimal opportunity to directly view nonanalytic behavior associated with the meson cloud of full QCD and the quenched meson cloud of quenched QCD. The u quark in Sigma^+ provides the best opportunity to display the artifacts of the quenched approximation.