The spherical alga Volvox swims by means of flagella on thousands of surface somatic cells. This geometry and its large size make it a model organism for studying the fluid dynamics of multicellularity. Remarkably, when two nearby Volvox swim close to a solid surface, they attract one another and can form stable bound states in which they waltz or minuet around each other. A surface-mediated hydrodynamic attraction combined with lubrication forces between spinning, bottom-heavy Volvox explains the formation, stability and dynamics of the bound states. These phenomena are suggested to underlie observed clustering of Volvox at surfaces.