Some experiments say it's one thing, and others say it's another... and they just don't seem to be very compatible with each other.
To resolve it, I checked in the latest Particle Data Book which they have online:
But incredibly, they even report two different overall values for it (each averages from a lot of different kinds of experiments), which are not within 1-sigma of each other.
If you look in the "Electroweak Model and Constraints on New Physics" document, they go over lots of different values for it, and then give an overall "global fit" value of 0.1217 +- 0.0017.
But then if you look in the "Quantum Chromodynamics" document, they give a whole lot of other values for it from a mostly different set of experiments (QCD-stuff) and get an overall weighted averaged value of 0.1176 +- 0.002. They mention that the smallest errorbars are on the lattice qcd results which may be pulling it down a bit... if you remove that and look at everything else, it goes up to 0.1185.
If you look on the table of "physical constants" they provide, it gives the 0.1176 number. I seem to see more papers that assume it's 0.118, but the odd thing is that the error bars on that are not quite as good. So are we just supposed to *ignore* all of the precision electroweak data?
The really strange thing is that they make no attempt to reconcile these two reports, contained within the same website and updated the same year, or average them together.
The most straightforward MSSM prediction for alpha_3, assuming an SU(5) GUT theory is 0.130. If you allow for the unknown threshold effects, this could vary by +- 0.01... agreement with either of them is really not as good as some people like to say, although the GUT-scale threshold effects could conceivably fix it. At least it's a hell of a lot better than the Standard Model SU(5) prediction of 0.073 +- 0.001! If you believe in any kind of GUT group up there, you at least have to have new physics somewhere, whether or not it's SUSY.