Higher-order topological insulators (HOTIs), a new horizon of topological phases of matter, host lower-dimensional corner or hinge states, providing important stepping stones to the realization of robust topological waveguides in higher dimensions. The nontrivial band topology that gives rise to the corner or hinge states is usually enabled by certain crystalline symmetries. As a result, higher-order topological boundary states are tied to specific corners or hinges, lacking the flexibility of switching and selecting. Here, we report the experimental realization of topologically switchable and valley-selective corner states in a two-dimensional sonic crystal. Such intriguing properties are enabled by exploiting the higher-order topology assisted with the valley degree of freedom. For this purpose, we realize a valley HOTI of second-order topology characterized by the nontrivial bulk polarization. Interestingly, the hosted corner states are found to be valley dependent and therefore enable flexible control and manipulation on the wave localization. Topological switch on or off and valley selection of the corner states are directly observed through spatial scanning of the sound field. We further design an arbitrary structure of complex patterns containing corners with various intersection angles, among which selected corners can be illuminated or darkened upon valley selection. The reported valley HOTI and the valley-selective corner states provide fundamental understanding on the interplay between higher-order topology and valley degree of freedom and pave the way for lower-dimensional valleytronics, which may find potential applications in integrated acoustics and photonics.