  We study the polarizations of gravitational waves (GWs) in two classes of
extended gravity theories. As a preparatory yet complete study, 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. When expanded around 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 coupling constants of HCG. In the analysis of HCG, 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.
