No, the volume of liquids and solids does depend on pressure. However, the volume of gases is drastically more sensitive to pressure. (This property is known as compressibility.)
In most contexts, the dependence of volume on pressure for liquids and especially solids is considered negligible (that is, most liquids and solids are approximately incompressible). In mathematical terms, this means $\frac{dV}{dP} \approx 0$ (the rate of change of volume with respect to pressure is essentially zero).
As before stated, the volume of gases depends significantly on pressure. In fact, in the ideal gas model (a good approximation for most gases), the two "state variables" are inversely proportional: $V \propto \frac{1}{P}$ (Boyle's Law).