A recent paper reviews the issue and ongoing efforts to obtain greater precision in both the experimental and theoretical estimates of the value of this physical constant.
The discrepancy is simultaneously (1) one of the stronger data points pointing towards potential beyond the Standard Model physics (with the muon magnetic moment approximately 43,000 times more sensitive to GeV particle impacts on the measurement than the electron magnetic moment) and (2) a severe constraint on beyond the Standard Model physics, because the absolute difference and relative differences are so modest that any BSM effect must be very subtle.
We are five to seven years from the point at which improved theoretical calculations and experimental measurements combined will either definitively establish a beyond the Standard Model effect, or rule one out to a much higher level of precision. My money, for what it is worth, is on the latter result.
The muon g-2 limitations on supersymmetry are particularly notable because unlike limitations from collider experiments, the muon g-2 limitations tend to cap the mass of the lightest supersymmetric particle, or at least to strongly favor lighter sparticle masses in global fits to experimental data of SUSY parameters. As a paper earlier this year noted:
There is more than 3 sigma deviation between the experimental and theoretical results of the muon g-2. This suggests that some of the SUSY particles have a mass of order 100 GeV. We study searches for those particles at the LHC with particular attention to the muon g-2. In particular, the recent results on the searches for the non-colored SUSY particles are investigated in the parameter region where the muon g-2 is explained. The analysis is independent of details of the SUSY models.The LHC, of course, has largely ruled out SUSY particles with masses on the order of 100 GeV. Another fairly thoughtful reconciliation of the muon g-2 limitations with Higgs boson mass and other LHC discovery constraints can be found in a February 28, 2013 paper which in addition to offering its own light sleptons, heavy squark solution also catalogs other approaches that could work.
Regrettably, I have not located any papers examining experimental boundaries on SUSY parameter space that also include limitations from the absence of discovery of proton decay of less than a certain length of time, and the current thresholds of non-discovery of neutrinoless double beta decay. The latter, like muon g-2 limitations, generically tends to disfavor heavy sparticles, although one can design a SUSY model that addresses this reality.
Some studies do incorporate the lack of positive detections of GeV scale WIMPS in direct dark matter searches by XENON 100 that have been made more definitive by the recent LUX experiment results. Barring "blind spots" in Tevatron and LHC and LEP experiments at low masses, a sub-TeV mass plain vanilla SUSY dark matter candidate is effectively excluded by current experimental results. And, other lines of reasoning strongly disfavor dark matter candidates with masses in excess of a TeV.