A 126 GeV Higgs Boson, which is rumored to have been seen (at a 4.3 sigma, not quite "discovery" standard), has major implications for beyond the Standard Model physics. It destroys the motivation for technicolor or a composite Higgs boson. It tends to disfavor a fourth generation of fundamental particles.
It undermines, without dealing a death blow to, supersymmetry (i.e. SUSY), and by implication, string theory, both because those models favor lighter Higgs bosons and because the justification for their existence is reduced if the Standard Model is stable at high energy levels.
It disfavors any introduction of new fundamental forces with any phenomenological impact.
It seems to be relatively neutral in its impact of extensions of the Standard Model with right handed or otherwise "sterile" neutrinos. It doesn't really have any strong implications for the notion of quark-lepton complementarity.
It leaves a void in the realm of fundamental dark matter candidates, which tends to make heavy stertile neutrino models and composite dark matter candidates attractive.
It doesn't necessarily have much impact on loop quantum gravity inquiries, or on the possibility of a spin-2 graviton stripped from a string theory context.
UPDATE: An exhaustive compilation of 81 recent published Higgs boson mass predictions as of June 2010, including 23 supersymmetric ones, shows what a parlor game this has become. Sixty-six of the predictions would be falsified by a 126 GeV Higgs boson, and many of the rest would be correct only by virtue of wide error bars. One of the many upper bounds would be invalidated, but only by a few GeV which would probably be within the error bars of the announcement a week from today. Fifteen predictions were consistent with this mass, although many of those predictions were consistent only by virtue of their wide error bars and were not particularly close to a 126 GeV predicted value.
In the supersymmetric theories, one of the effects of finding a "lightest Higgs boson mass" (generically, SUSY models tend to have more than one Higgs boson), is that it fixes one of two key constants from which supersymmetric particle masses are derived in these models, dramatically constraining the mass spectrum of the other particles and as a result, making falsification of the models from failure to find other supersymmetric particles in the expected mass ranges much easier.
The Minimal Supersymmetric Standard Model (MSSM), originally proposed in 1981 as the first supersymmetric model, predicted the exitence of new particles in the 100 GeV to 1000 GeV range, and is already a stretch considering experimental bounds already in existence on the existence of such particles and its need for a light Higgs boson mass, but less minimal SUSY theories aren't ruled out at this point. In addition to providing high lower bounds on the masses of the lightest supersymmetric particles, the LHC has also largely ruled out "R-party conserving" models of supersymmetry.
At the very least, the LHC has established that all supersymmetric particles are heavier than than all non-supersymmetric particles by a considerable margin.