As coconut wrote, the superposition principle comes from the linearity of the operator involved. This is the case for water and sound waves, as well as for electromagnetic radiation in vacuum. Approximations to water waves are also linear (since it is an approximation) but probably will have small non-linear parts. Free quantum field theory is also linear, therefore you have a superposition principle there. With interactions and renormalization, I think it is not linear any more.
Gravity as described by general relativity is highly non-linear. Therefore it does not have any superposition principle. Gravitational waves do not have a superposition principle. However, at very large distances these waves can be approximated. And then this operator might be linear and you can reasonable speak of superpositions again.
The usual approximation to a wave, $$ \left(\frac{1}{c^2} \frac{\mathrm d^2}{\mathrm dt^2} - \nabla^2 \right) \phi(x, t) = 0 \,$$ is linear by definition. A lot of waves can be described well as linear waves with non-linear perturbations (water waves, EM waves in medium). Strictly speaking, they are non-linear from the start once there is the smallest non-linear perturbation to them.