Metasurfaces with subwavelength thicknesses have exhibited unconventional phenomena in ways that could not be mimicked by traditional materials. Here we report on the analytical design and experimental realizations of acoustic metasurfaces with hitherto inaccessible functionality of manipulating the reflected waves arbitrarily. By suitably designing the phase-shift profile with a 2π span induced by labyrinthine units, the metasurface can reflect acoustic waves in an unusual yet controllable manner. Anomalous reflection and ultrathin planar lenses are both demonstrated with carefully designed metasurfaces. Remarkably, the free manipulation of phase shifts offers great flexibility in the design of nonparaxial acoustic self-accelerating beams with arbitrary trajectories. With extraordinary wave-steering ability, the metasurface should open exciting possibilities for designing compact acoustic components with versatile potential and may find a variety of applications ranging from ultrasound imaging to caustic engineering where designing the shape of a focused trajectory of sound is required.