  Luttinger's theorem for Fermi liquids equates the volume enclosed by the
Fermi surface in momentum space to the electron filling, independent of the
strength and nature of interactions. Motivated by recent momentum balance
arguments that establish this result in a non-perturbative fashion [M.
Oshikawa, Phys. Rev. Lett. {\bf 84}, 3370 (2000)], we present extensions of
this momentum balance argument to exotic systems which exhibit quantum number
fractionalization focussing on $Z_2$ fractionalized insulators, superfluids and
Fermi liquids. These lead to nontrivial relations between the particle filling
and some intrinsic property of these quantum phases, and hence may be regarded
as natural extensions of Luttinger's theorem. We find that there is an
important distinction between fractionalized states arising naturally from half
filling versus those arising from integer filling. We also note how these
results can be useful for identifying fractionalized states in numerical
experiments.
