As for references to other approaches to the foundations of Statistical Physics, you can have a look at the classical paper by Jaynes; see also, e.g., this paper (in particular section 2.3) where he discusses the irrelevance of ergodic-type hypotheses as a foundation of equilibrium statistical mechanics. Of course, Jaynes' approach also suffers from a number of deficiencies, and I think that one can safely says that the foundational problem in equilibrium statistical mechanics is still widely open.
You may also find it interesting to look at this paper by Uffink, where most of the modern (and ancient) approaches to this problem are described, together with their respective shortcomings. This will provide you with many more recent references.
Finally, if you want a mathematically more thorough discussion of the role of ergodicity (properly interpreted) in the foundations of statistical mechanics, you should have a look at Gallavotti's Statistical Mechanics - short treatiseStatistical Mechanics - short treatise, Springer-Verlag (1999), in particular Chapters I, II and IX.
EDIT (June 22 2012): I just remembered about this paper by Bricmont that I read long ago. It's quite interesting and a pleasant read (like most of what he writes): Bayes, Boltzmann and Bohm: Probabilities in Physics.