It is common knowledge that surfactants lower the surface tension of water. The typical textbook explanation of this phenomenon is that the force of attraction between surfactant and water molecules is less than that between two water molecules; hence the surface contraction force decreases in the presence of surfactants; however, this common description, based on the strength of intermolecular interactions, is overly simplified because it ignores an important thermodynamic function: the surface entropy of water. Here we report separate measurements of water's surface enthalpy and surface entropy in the presence of nonionic, zwitterionic, anionic, and cationic surfactants. While all of these surfactants decreased the surface enthalpy of water by 50-70%, the surface entropy of water could drop to near-zero or even negative values for ionic surfactants. Studies of this zero-entropy state of water surface using phase-sensitive sum-frequency generation (SFG) vibrational spectroscopy and molecular dynamics (MD) simulations suggested that the zero-entropy state of the water surface was associated with surfactant-induced ordering of water molecules and enhanced hydrogen bond formation at the water surface. Both effects reduce water molecules' degrees of freedom for motion and thus lower the surface entropy of water. The ability of a surfactant to decrease the surface entropy of water is in the order ionic > zwitterionic > nonionic. For all surfactant head groups surface entropy plays a critical role in determining the surface tension of water. The description of water's surface tension is not complete without considering its surface entropy.