Motl expands on the implications of a Higgs boson of this mass in this post. A money quote:
One may say that 125 GeV is exactly the borderline between the "visible SUSY" for very low masses and the "SUSY in the closet" for somewhat heavier Higgs masses.
If the Higgs mass is above 125 GeV, models with a high energy supersymmetry breaking scale become favored. They include many natural E 6 grand unified theories and extensions of the minimal supersymmetric standard model (MSSM) with extra multiplets (when we add a single scalar field, we get the so-called NMSSM, where N stands for "next to"). . . .
Quite generally, these models – much like Kane-led M-theory phenomenology – assume that most of the scalar superpartners (superpartners of known fermions) have masses between 20 and 100 TeV or so. The fermionic superpartners (gauginos and Higgsinos) may be much lighter and some of them are often (predicted to be) accessible at the LHC. The third generation of squarks (and sometimes sleptons) is usually somewhat (or much) lighter than the first two generations, exactly in the opposite way than for the known quarks and leptons.
Some of these models try to promote different philosophies and personal twists but a big part of their message is overlapping. The LHC should see a Higgs most likely in the 120-135 GeV window and there could be new physics, most likely some fermionic superpartners of the known gauge bosons (or the Higgs) that should still be accessible. Many of the details remain unknown. It's not guaranteed that the LHC will see something beyond the 125 GeV Higgs boson but I think it's rather likely and so does my Princeton source.
FWIW, I think it is rather likely that the LHC will see no new physics whatsoever beyond the Higgs boson, although it will almost surely refine the values we have for various constants of the Standard Model, may refine the beta functions used to describe the running of the coupling constants of the three Standard Model forces, and may expose one or two bad assumptions that are currently widely used in approximating the predictions of the Standard Model from its current equation set. In my view, the Higgs boson find that is widely anticipated greatly reduces the experimental motivation and theoretical imperative to solve "naturalness" concerns about the Standard Model, related to vacuum instability at high energy levels, with SUSY. Post-Higgs, the biggest piece of uncharted Standard Model territory left is in neutrino physics and it isn't obvious that the main two collaborations at the LHC are doing the kind of work that will answer those questions.
Motl also notes a not very impressive rebuttal to String Theory/M Theory critics that says many nice things about unexpected benefits of String Theory methods outside fundamental physics, and positions String Theory as a theory at least as plausible as any alternative theoretical program, but fails to rebut the key point of the critics which is the absence of an experimental justification for String Theory's dominance as a BSM theory taken seriously in academic faculties and in matters like analysis of big dollar collider results against that theory's predictions.
While I'm add it, I will also note one of those other BSM theories,