No, not the kind of Singularity usually discussed here... I'm referring to the possibility of phantom energy-driven rips in the cosmos caused by accelerating expansion, or "sudden future singularities of pressure". (Technically: "a momentary infinite peak in the tidal forces of the universe.") A recent paper by Ghodsi & Hendri shows that cosmic microwave background, baryon acoustic oscillations (BAO), and type 1a supernovae data is consistent with the possibility of a sudden future singularity as soon as 8.7 million years from now.
"Cosmological tests of sudden future singularities"
As I understand it, the authors are not saying that a SFS is likely 8.7 million years from now, just possible. This puts a dampener on the notion that the only plausible scenario of cosmological breakdown is Heat Death.
Here's another paper that outlines other exotic cosmological singularities which have been under discussion in the cosmology community for the past decade, and the behavior of pointlike particles and strings as they approach such singularities.