The situation in astrophysics is completely different. Almost every respectable experiment can boast of an unexplained excess, a mysterious bump or a striking anomaly. Part of the reason is that, in astrophysics, backgrounds are often as good as unknown while the error bars are estimated by throwing dice. But, hopefully, this is not the whole story. In the end, the only clear evidence for physics beyond the Standard Model comes from astrophysical observations that have established the existence of dark matter. There is actually more dark than ordinary matter in the sky, and it is quite likely that some of the puzzling results below are in fact messages from the dark sector.
Here is a collection of astroparticle anomalies directly or indirectly related to dark matter searches. In my subjective order of relevance.
It finally happened: SUSY is no longer the favorite hottie, all eyes are now on PAMELA (although some attempt dating both). PAMELA is a satellite experiment who measures the cosmic flux of anti-protons and positrons. While the former flux is roughly consistent with theoretical estimates, the positron flux displays a steep rise at energies above 10 GeV, contrary to expectations based on the secondary production of positrons by cosmic rays scattering on interstellar matter. The simplest interpretation of the PAMELA excess is that the background is not properly estimated, and for the moment this remains a perfectly viable option. Another possibility is that the positron spectrum is contaminated by a nearby astrophysical source like a pulsar or a micro-quasar. Finally, the excess could be a manifestation of dark matter.
The PAMELA positron excess can be explained by a dark matter particle who is heavier than 100 GeV and annihilates preferentially into the Standard Model leptons, with the annihilation into hadrons suppressed down to the rate of 10 percent or less. A slightly more exotic scenario is that dark matter is not stable but decays into leptons, which amounts to pretty much the same from the point of view of indirect detection.
If one naively continues the slope in the PAMELA spectrum beyond 100 GeV, the positron fraction above a few hundred GeV becomes of order one. That energy range is probed by ATIC - a balloon experiment detecting cosmic electrons and positrons (without being able to distinguish the two). And indeed, ATIC observes an excess of electrons at positrons at energies between 100 and 800 GeV. The size of the effect nicely fits with the PAMELA excess, and it is very likely that both observations have the common origin (whether it is dark matter or not). Moreover, ATIC observes a clear feature in the spectrum - a bump around 600 GeV followed by a sharp decline above 800 GeV (the latter recently confirmed by HESS). If this features are indeed signals of dark matter, the ATIC observation pinpoints the mass scale of the dark matter particle to be around 1 TeV. A good news for the LHC.
It may be worth mentioning that the ATIC peak is inconsistent with another experiment called EC who studied the similar energy range but found no excess. On the other hand, ATIC is consistent with the results from PPB-BETs, but that experiments is generally dismissed due to its miniature size (it was manufactured by Japanese). The rumor is that the new ATIC-4 data will confirm the peak and reduce the error bars by a factor of two.
The WMAP satellite made its name studying the primordial microwave spectrum produced at the early hot stage of the Universe. The microwave emission from our galaxy is an annoying background (or foreground, depending which way you look) and has to be carefully studied too. Our galaxy pollutes the CMB via thermal dust emission, thermal bremsstrahlung, synchrotron radiation and spinning dust. Subtracting these known contributions revealed the presence of an additional component that extends some 30 degrees around the galactic center. This excess can be interpreted as the synchrotron radiation of electrons and positrons produced by dark matter in the galactic center (that's where the dark matter density is the largest). By itself, the Haze is maybe not an overwhelming evidence for dark matter, but in the light of PAMELA and ATIC it is another indication that too many positrons and/or electrons are flying around. Besides, it has a cool name.
EGRET was a cosmic telescope that studied diffuse gamma-ray emission in the 30 MeV - 100 GeV range. Excessive emission from the galactic center at energies between 10 and 50 GeV was concluded in this paper. The excess can be interpreted as another manifestation of dark matter annihilation or decay that produces high-energy electrons and positrons. The latter produce high-energy photons via inverse-Compton scattering of starlight or of the microwave background.
The INTEGRAL satellite detected the 511 keV gamma-ray line from the galactic center. Photons carrying 511 keV energy arise from the e+e- annihilation at rest. If dark matter annihilation is the origin of this line, the dark particle must have rather non-trivial properties to produce electrons and positrons nearly at rest: either its mass is in the MeV range, or it has an excited state with a 1-2 MeV splitting. The most recent results from INTEGRAL weakened the case for dark matter. The new observations display an asymmetry of the emission with respect to the central axis of the galaxy which seems to be correlated with the distribution of low mass X-ray binaries - systems including a neutron star or a black hole that accretes matter from its companion. At this point a conventional astrophysical explanation seems far more likely, but the case is not closed yet.
All the previous observations, when interpreted in terms of dark matter, fall into the class of indirect detection, that is observations of the final products of dark matter annihilation or decay. The complementary technique, called direct detection, consists in searching for signals of dark matter particles scattering on a target made of ordinary Standard Model particles. There are many direct detection experiments going on: CDMS, XENON, CRESST, DAMA to name a few active ones. The last one actually claims a detection. Unfortunately, this is the one we trust the least. The reason is that DAMA's detection technique cannot effectively distinguish dark matter particles from a huge background of ordinary particles scattering on the target. Instead, the claim is based on observing the annual variation of the signal which may be induced by a variation of the dark matter flux due to the motion of the Earth around the Sun. The size of the effect observed by DAMA is however in conflict with other direct detection experiments, unless the dark matter particle has some contrived properties (for example, an excited state with a 100 keV splitting). Another viable interpretation of the DAMA signal is that the Italian mafia dumps radioactive waste near Gran Sasso every year in June. Or there is some other regular effect with an annual period. Most likely, DAMA will share the fate of LSND: we will never what went wrong.
That's it. As a homework, try to fit all six anomalous results in a single theory of dark matter (solution here). But be careful. A wise man once said that if a theory can explain all experimental results then it is certainly wrong. Because some experiments are always wrong.