The anomalous g-factors of the muon and electron have played an important role in the development of QED, and in our understanding of the nature of these leptons. The current precision of the electron anomaly makes it one of the most precisely measured quantities in nature, and one could argue that QED is so well understood that this measurement can be used to provide the best measurement of the fine-structure constant.
The muon g-factor has measurable contributions from virtual hadrons, and soon we hope to measure the W and Z 0 gauge boson contributions. This new measurement also opens a window for the discovery of new physics beyond the standard model. For a full interpretation of this experiment, additional data, and calculations, will be needed to permit a more precise evaluation of the hadronic vacuum polarization contribution to a μ.
Baryon magnetic moments is another subject altogether. Because of the difficulties of calculating low energy phenomena in QCD, it is necessary to resort to QCD inspired phenomenological models, which describe the situation to about 10%, decades away from the spectacular agreement between theory and experiment for the leptons. Nevertheless, when the constituent quark models were being developed in the 70s, hyperon magnetic moments played an important role in testing their validity. Perhaps some day, computing power will increase to the point where lattice calculations of the static baryon properties can reach an accuracy which would permit a meaningful comparison with experiment.