When tea is poured from a teapot it often runs along the under side of the spout rather than falling into the cup. Recent experiments have shown that this ``teapot effect'' is not due to surface tension nor adhesion, as many have supposed. Therefore, a new explanation is presented which is based upon certain exact solutions of the hydrodynamic equations and which seems to account for the effect. In connection with the analysis some new fluid flows with free boundaries are obtained. In addition a method more satisfactory than the usual one is used to study the stability of these flows.