What is the cosmic "Axis of Evil" problem? What is the cosmic "axis of evil" problem?
Apparently it is a more modern version of the old cluster mass discrepancy problem, where masses determined by gravitational lensing are always higher than masses determined by X-ray observations.
Now Sunyaev-Zeldovich (SZ) masses from Planck seem to make the problem worse. Do the SZ masses disagree with both the lensing masses and the X-ray temperature masses?
 A: The "axis of evil" is a peculiar alignment between the large angular scale properties of the cosmic microwave background and a number of other features in the large scale structure of the local Universe. Schild & Gibson (http://arxiv.org/abs/0802.3229) summarize it as:

Soon it was also found that the axis [in the CMB] points toward an unexpectedly large low-temperature structure in the background radiation (Vielva et al. 2004), and then that this void is very significantly deficient in radio galaxies (McEwen et al. 2006, 2007; Rudnick et al. 2007). Finally, polarizations of quasars (Hutsemekers et al 2005) and analysis of the spins of spiral galaxies catalogued in the SDSS, showed that they display a statistically significant alignment, in the sense that observed spiral structure in galaxies prefers a significant sense (handedness) along this same axis (Longo 2007).

The name is one of those evocative, if rather inaccurate, names that catch on in Astronomy (cf. Big Bang, Black Hole, etc.) - there's nothing "evil" about it. I get the feeling that the consensus is that it's a chance effect based primarily on the inherent difficulty in measuring the CMB power at large angular scales, but i'm not very in touch with Cosmology these days.  
edit: regarding what the "problem" is, cold dark matter cosmology has no expectation or reason for such an alignment; if there is a bona fide correlation then it might imply our current cosmological model is incorrect. 
A: Update:
As of March 21, 2013, with the Planck confirmation of the Axis, it is clearly not a chance effect based primarily on the inherent difficulty in measuring the CMB power at large angular scales.
The effect is real, and indeed, presents what could turn out to be a very big problem indeed for the standard (LCDM/inflation)cosmological consensus.
The fact that the alignments are with respect to our location is utterly astounding, and is being assiduously avoided for obvious reasons.
