There is a forthcoming paper which claims the discovery of two particles decaying into electron pairs, which are tentatively identified as axions, with masses of 7 and 19 MeV respectively.
I am a little sceptical of this claim, based as it is on two narrow peaks being 3 standard deviations above the best fit to the background. I'm no experimentalist, but the situation appears to me to be too similar to the "discovery" of the pentaquarks, which later dissolved into statistical fluctuations as better data became available.
If this discovery turns out to be real, though, this would be huge news: the discovery of the axion would solve the strong CP problem (why is the CP-violating θ-angle in QCD so close to, or even identically, zero, when it generically should be of order one?) and might also contribute to solving the riddle of dark matter. There are a number of experiments looking for the axion, the best known being PVLAS, who claimed to have found a candidate with a mass in the meV (milli-eV) range, and the new experiments at CERN aiming to test their results.
So we should wait and see if axions have indeed been observed. If so, it would be great news for theoretical particle physics: it would be, as far as I am aware, the first discovery of a particle whose existence was conjectured based on naturalness considerations alone. If not, it would show once again that results based on low statistics should always be taken with great care.
Update: More criticism (by experimentalists) of the claimed discovery can be found on Chad Orzel's blog and on Superweak.