Ten preprints were filed explaining the 750 GeV bump the day that it was announced (which is most often abbreviated as a particle described with the symbol S (for scalar)) and eight more preprints were filed the following day. UPDATE December 20, 2015: Twenty more papers were posted on the 18th. In addition, both Jester and Marco Frasca have advanced interpretations not clearly expressed in preprints in their respective blogs. The six Higgs bosons theory was also noted and dismissed without meaningful analysis by Lubos Motl at his blog.
Marco Frasca is the only voice out there arguing that there is any way that this bump could be consistent with the Standard Model Lagrangian by any means other than the six Higgs boson route, and thus has staked out what is for the most part the most conservative take on the news. Of course, there are lots of voices out there arguing that it isn't too late for the 750 GeV bump to turn out to be a fluke with the 145 GeV potential Higgs boson bump in the early days of the LHC which was offered up as a very comparable bump in terms of significance and character that didn't end up amounting to anything in the end.
In addition to the theories that I have described previously, the possibility that this is an axion, a graviton-like particle, or a Goldstone boson associated with supersymmetry breaking (or superpartner of one) have been raised. Composite particle analysis has been extended to consider a heavy pion or pion-like composite particle.
Still, to mangle an old saw, publication is the most sincere sign of credibility. We would not be deluged with the amount of fairly high quality instant analysis (often with multiple authors) that we have seen in the last couple of days if professionals in the HEP community weren't taking the 750 GeV bump very seriously.
I am inclined to think that the assumption that any tensor particle that can decay to a diphoton must be a graviton of some type, made by many of commentators is wrong (e.g. consider the counterexample to prove the point even if it isn't particularly likely, of a highly excited tensor glueball). Also though it is worth noting that any particle with neutral electric charge that can decay in a diphoton mode must do so through a triangle diagram, because neutral particles themselves don't couple to photons.
There is a definite "who ordered that" air to the entire discussion. While multiple papers have proposed some relationship between this bump and dark matter, it is far too heavy to be a credible dark matter candidate or and is far too heavy to even be a credible dark matter self-interaction force carrying boson. And, there really isn't any phenomenology gap other than the appearance of the bump itself, that we need to explain with this particle or something very much like it. This particle does not naturally recommend itself to solving any of the important unsolved questions in physics that we were looking for solutions to when it was observed.
Also, I should mention that the announcement also places strict limits on SUSY theories with many of the preprint authors acknowledging that the 750 GeV bump, if true, completely rules out the entire parameter space of the Minimal Supersymmetric Standard Model (MSSM). String theorists and SUSY supporters have retreated to the NMSSM (next to minimal supersymmetric standard model) barricades for the time being.
* Meson width (which is the inverse of half-life in the proper units) is related to temperature under some leading numerical approximations of QCD by as much as a factor of fifty. This result could be relevant to the many questions that have arisen over whether the 750 GeV bump is consistent with a Higgs like boson based upon its width, as the unprecedented energy scales of the latest data may have an impact on effective temperature which in turn can influence width and has probably not been widely adjusted for by early commentators.
* The never ending battle to measure the QCD coupling constant continues, although its current accuracy isn't that impressive. The current world average is down a bit to 0.1177 +/- 0.13 (about 1%) which is down by about 0.0007 from the previous world average. The real interesting question, however, is not the actual mean value of the QCD coupling constant (even though that is more interesting than it seems), but whether the running of the QCD coupling constant with energy scale is consistent with the Standard Model prediction, or differs as it does in almost all grand unification theories including SUSY.
META NOTE: With this post, both Dispatches at Turtle Island and its sister blog Wash Park Prophet have more posts in 2015 than they did in either 2014 or 2013.
UPDATE December 19, 2015: A 750 GeV Higgs boson could secure that vacuum stability that is merely metastable with a single 126 GeV Higgs boson.