To my knowledge, although there exist similar approximations in other fields, nowhere they are as developed as WKB in quantum mechanics.
Perhaps, adiabatic approximation is the most general term, as it is applied to WKB but also to some other problems (e.g., classical charges moving in slowly varying magnetic fields in synchrotrons, etc.)
Eikonal approximation is another method that is often compared to WKB, but which has its roots in more general wave theory (e.g., ray optics.) But the main idea has more to do with the method of characteristics than with the slow change (it is not even always approximate.) See also derivation of geometric optics by Sommerfeld-Runge method.
Finally, in studying wave propagation in random media one uses sometimes diffusion approximation to wave or Poisson equation - but this is a rather exotic example in my opinion (unless you work in the field.) See, e.g., On waves in random media in the diffusion-approximation regime
Update
This old question, raised today by the community bot, reminded me of another often overlooked example of slowly varying quantities: envelope function approximation. In crystals we will often consider only a single band, $\epsilon_c(\mathbf{k})$, treating the crystal quasimomentum $\mathbf{k}$, as if it were true momentum $\mathbf{p}$. In real space representation (rather than in quasimomentum representation) this means that we are working with wave-functions that are slowly varying over the extent of many unit cells. This is often accompanied by expanding the dispersion relation near its singular point, producing the effective mass approximation or Dirac cones in graphene/metallic carbon nanotubes.
The next layer in this approximation is imposing external fields, which often break the translational symmetry (see Volume 9 of Landau&Lifshitz for discussion of the magnetic field in crystal.) However, when these fields are slowly varying (i.e., adiabatically varying) over many lattice spacing, we can still treat the Hamitronian as that of a free particle, notably using Peierls approximation.
$$
\epsilon_c(\hbar\mathbf{k})\rightarrow \epsilon_c(\mathbf{p})\rightarrow\epsilon_c(-i\hbar\nabla)\rightarrow
\epsilon_c\left(\mathbf{p}-\frac{e}{c}\mathbf{A}\right)$$
Another example, involving slowly varying order parameter (but often treated as a wave function) is Ginsburg-Landau theory for describing superconductivity.
This then branches onto the procedures associated with coarse-graning in order to introduce consistently the mean-field theory (see Lectures on phase transitions and renormalization group by Goldenfeld), and quasi-equilibrium approximation used to obtain hydrodynamic equations from the kinetic theory of gases, see this answer and this one.
