μ- → e- + γ or μ+ → e+ + γSo far, no reliable evidence of such a flavor-changing decay has been observed. That's also true for the MEG experiment as of May 2010. The upper bound on the branching ratio is something like "at most 10-30 parts per trillion" among the decays of muons end up with electrons and photons.
Experimentally accessible decays of the muon are predicted by supersymmetry - and perhaps other beyond-the-Standard-Model physics scenarios. The detailed fraction of the decays with this fate depends on unknown values of various parameters.
However, the Symmetry Breaking Magazine just published something that could be interpreted as a positive rumor about a signal:
MEG experiment may give boost to supersymmetryCandidate events for muons decaying to electrons have been seen but they're not enough to claim a discovery. It's being promised that an interesting paper could be published in Summer 2011 when the amount of data gets doubled - relatively to a point when it was just one half of it. ;-) The experiment is designed to decide about branching ratios as small as 10^{-13} - one part per ten trillion.
America's Fermilab will start the construction of its own muon-to-electron experiment, Mu2e experiment, in 2013 - in the post-Tevatron era. But the data over there will only be collected around 2017.