See Ostvaer for an introduction to maps from algebraic K-theory to Hochschild homology (Dennis trace map), topological Hochschild homology, and topological cyclic homology (cyclotomic trace map). These fit into a commutative diagram with maps from TC to THH and from THH to HH.
Karoubi and Lambre on the Dennis trace map and algebraic number theory.
Nistor on the Hochschild homology of Hecke algebras
Hochschild, Kostant, Rosenberg: Differential forms on regular affine algebras. (Does this belong in this page???)
Chapter 9 in Weibel: An introduction to homological algebra.
arXiv: Experimental full text search
NCG (Algebra and noncommutative geometry)
Cortinas and Weibel: Homology of Azumaya algebras. Describes the Hochschild homology of Azumaya algs. It seems like there is a “reduced trace map isomorphism” between the HH of a matrix algebra over a ring and HH of the ring.
Kazhdan et al: http://www.math.uiuc.edu/K-theory/0222
K-regularity, cdh-fibrant Hochschild homology, and a conjecture of Vorst , by G. Cortinas , C. Haesemeyer , and C. A. Weibel: http://www.math.uiuc.edu/K-theory/0783
E_n homology as functor homology http://front.math.ucdavis.edu/0907.1283
Talk by Greg Ginot - Derived Higher Hochschild theory. Abstract: Recently, various homology (or rather objects of some derived category) inspired by topological field theories have emerged, for instance Costello-Gwilliam factorization algebras. Another one of this is given by higher Hochschild homology; this is a (derived) bifunctor associated to topological spaces and commutative differential graded algebras (=CDGA) with value in CDGA, which coincides with the usual Hochshcild complex when applied to a circle. We gave an axiomatic characterization of this bifunctor (as well as some nice corollaries of it) and explain its close relationship with locally constant factorization algebras. The key idea is to use a locality axiom which also implies a close relationship with Lurie’s Topological chiral homology.
For a def in a very general context, see http://mathoverflow.net/questions/55018/tropical-homological-algebra
http://mathoverflow.net/questions/3078/how-exactly-is-hochschild-homology-a-monad-homology
http://mathoverflow.net/questions/39726/hochschild-homology-of-dgas
nLab page on Hochschild homology