  We study the polarizations of gravitational waves (GWs) in two classes of
extended gravity theories. First, we formulate the polarizations in linear
massive gravity (MG) with generic mass terms of non-Fierz-Pauli type by
identifying all the independent variables that obey Klein-Gordon-type
equations. The dynamical degrees of freedom (dofs) in the generic MG consist of
spin-2 and spin-0 modes, the former breaking down into two tensor (helicity-2),
two vector (helicity-1) and one scalar (helicity-0) components, while the
latter just corresponding to a scalar. We find convenient ways of decomposing
the two scalar modes of each spin into distinct linear combinations of the
transverse and longitudinal polarizations with coefficients directly expressed
by the mass parameters, thereby serving as a useful tool in measuring the
masses of GWs. Then we analyze the linear perturbations of generic
higher-curvature gravity (HCG) whose Lagrangian is an arbitrary polynomial of
the Riemann tensor. On a flat background, the linear dynamical dofs in this
theory are identified as massless spin-2, massive spin-2, and massive spin-0
modes. As its massive part encompasses the identical structure to the generic
MG, GWs in the generic HCG provide six massive polarizations on top of the
ordinary two massless modes. In parallel to MG, we find convenient
representations for the scalar-polarization modes directly connected to the
parameters of HCG. In this analysis, we employ two distinct methods; One takes
full advantage of the partial equivalence between the generic HCG and MG at the
linear level, whereas the other relies upon a gauge-invariant formalism. We
confirm that the two results agree. We also discuss methods to determine the
theory parameters by GW-polarization measurements. Our method does not require
measuring the propagation speeds or the details of the waveforms of the GWs.
[Abridged]
