  We show that polarization singularities, generic for any complex vector field
but so far mostly studied for electromagnetic fields, appear naturally in
inhomogeneous yet monochromatic sound and water-surface (e.g., gravity or
capillary) wave fields in fluids or gases. The vector properties of these waves
are described by the velocity or displacement fields characterizing the local
oscillatory motion of the medium particles. We consider a number of examples
revealing C-points of purely circular polarization and polarization M\"{o}bius
strips (formed by major axes of polarization ellipses) around the C-points in
sound and gravity wave fields. Our results (i) offer a new readily accessible
platform for studies of polarization singularities and topological features of
complex vector wavefields and (ii) can play an important role in characterizing
vector (e.g., dipole) wave-matter interactions in acoustics and fluid
mechanics.
