The turbulent fountain that results from the injection of a dense fluid upwards into a large tank of stably stratified fluid of lower density is studied experimentally and theoretically. For both axisymmetric and line fountains, we have used a combination of dimensional arguments and laboratory experiments to determine the initial height above the source at which the flow first comes to rest. Depending on the strength of the stratification and the fluxes of momentum and buoyancy at the source, the subsequent down flow may either spread along the base of the tank or intrude at an intermediate height in the environment. We determine both the height of intermediate intrusion and the critical condition for spreading along the base. We also relate numerical solutions of the entrainment equations to our experimental observations, and obtain effective entrainment coefficients for both axisymmetric and line fountains. Finally, we discuss the quantitative application of our results to the replenishment of magma chambers and to the heating or cooling of a room.