Both ATLAS and CMS have announced new data on tau-tau decays of the Higgs, providing stronger evidence for this signal than was available earlier. ATLAS sees a signal with significance 4.1 sigma, CMS at 3.4 sigma. These results are consistent with the SM, and rule out some SUSY alternatives in which the Higgs would behave differently. The Register headlines this Exotic physics takes an arrow to the knee.Relative to the Standard Model expectation, at ATLAS the signal seen is 140% of the Standard Model value with margins of error to fit values between 100% and 190% of it. At CMS, the signal seen is 87% of the Standard Model value with margins of error to fit between 58% and 116% of it.
The opposite direction of deviation from the Standard Model expectation value at two experiments simultaneously measuring the same thing discourages speculation that the true value differs materially in one direction or the other from the Standard Model Higgs boson tau-tau decay rate. Most importantly, this result strongly disfavors speculative theories like a "leptophobic" or "leptophilic" Higgs boson that couples with different strengths relative to mass to different kinds of particles.
There are five kinds of decays that should be observable from the Higgs bosons (there are other kinds as well but they are expected to be vanishingly rare). The discovery of the Higgs boson was based upon three of these decay channels, but the existence of Higgs boson decays in the tau-tau decay channel (a particle-antiparticle pair of third generation heavy electrons) and bottom-bottom (third generation down type quarks) channel remained less clear. There was a three sigma signal of bottom-bottom decays from Higgs bosons at Tevatron before it was shut down (this is actually the main decay channel of Higgs bosons, but is harder to identify due to large backgrounds from other processes), but there was less data on the tau-tau channel.
In absolute terms, particular channels of Higgs boson decays have mostly been within about 50% of the expected values, which is within two sigma due to large margins of error. Now that we have some reasonably significant observations in every expected decay channel and so far have not seen any unexpected decay products, the room for a non-Standard Model-like Higgs boson result narrows greatly.
Now, there is five plus sigma evidence of a Standard Model Higgs in three channels, better than four sigma evidence in the tau-tau channel, and three sigma evidence in the b-b channel. But, the relative uncertainty in the b-b channel makes it hard to pin down the total decay spectrum of the Higgs boson experimentally. If the b-b decay channel, for example, made up 55% rather than the expected 60% or so of expected Higgs decays, that would provide "room" for all sorts of other unexpected decays, so long as they don't involve W bosons or Z bosons or photons or charged Standard Model leptons.
The Standard Model predicts the probabilities of each of the Standard Model Higgs boson decay channels to a precision of something on the order of 1% of less for a Higgs boson with a mass known to the precision that it has been measured to date, so the prediction that the Standard Model Higgs will decay in a particular way is eminently testable.
Impact on Supersymmetry
Fortunately, many of the leading alternatives to the Standard Model, like supersymmetry (SUSY), also make quite specific predictions about how a spin-0 Higgs boson with zero electromagnetic charge and the observed mass (one of three or more neutral Higgs bosons present in SUSY theories), will behave in particular kinds of decay channels like tau-tau.
These models have moving parts (adjustable parameters) that can be used to tweak the predictions to the observed result, but the class of SUSY theories in which there is a Higgs boson that looks exactly like the Standard Model one and there are no other light Higgs bosons that can be detected with the searches that LHC has done so far is quite narrow (see also here).
The CMSSM version of SUSY, for example, isn't quite ruled out yet (and has a Higgs boson almost indistinguishable from the Standard Model Higgs boson), but is left to a steadily shrinking parameter space as SUSY particle exclusions from LHC grow larger and the anomalous magnetic moment of the muon limits how heavy its particles can get to evade LHC lower mass sparticle exclusions.
In a nutshell, it is becoming harder and harder for SUSY proponents to explain why there is still no meaningful experimental evidence of any of the myriad new particles that the theory implies. While it is easy to devise a SUSY theory in which most of the particles are too heavy to ever be detected, it is much harder to devise one where none of them are so light that they are observable or will soon be observable.
UPDATE December 10, 2013:
Another paper rules out a cascade of SUSY Higgs bosons into the observed phenomena with experimental evidence and also places the limits on the cross-sections o$f any SUSY Higgs boson phenomena at the LHC.