Why is water surface smooth? Liquids have more disorder than solids. Their atoms are much more jiggly than solids, at the same temperature. How then a puddle of water undisturbed by winds etc is able to have a smooth surface?
 A: Surface tension.
A molecule/atom of the liquid minimises its energy by being surrounded by other molecules/atoms of the liquid. At the surface this isn't possible so the surface has an excess energy, and this interfacial energy produces a force called surface tension that tries to reduce the area of the surface. There is a fuller discussion of this in my answer to Why is Sticking to Glass a Lower Energy State for Water?.
The tendancy to reduce the surface are is why liquid droplets are round, because spherical shape minimises the surface area for any given volume. It also means the surface will be smooth because any roughness increases the surface area and therefore increases the energy.
The surface will not be precisely smooth because we expect that thermal vibrations will produce deformations of the surface with energies of the order of $kT$ per surface molecule. At a macroscopic scale these deformations are too small to see, but at the atomic scale the surface will be fuzzy rather than sharply defined.
A: Surface tension.
Even at the microscopic level you would not see any motion at the surface, though if the water is unevenly heated there would be currents.  
A: To elaborate on Peter's answer.
It is precisely because water molecules are 'jiggly' that the surfaces are smooth.
Surface deformities cost (free) energy and so a system will only exhibit them if kinetically trapped (like the atoms in a solid are). But since the water molecules are free to flow, they don't get trapped in these high energy configurations and can instead achieve lower energy states (smooth surfaces).
A: Puddles are just a congregate of fluid molecules. True that they have greater disorder than solids, but therr are also stuff like viscous drag, and cohesive/adhesive forces in play(in the most simplest scenario). Surface tension is a result of the last 2. There are microscopic motions in a fluid continuosly(which is the reason behind the famous brownian motion), but without sufficient energy, a finite volume of a liquid cannot overcome the viscous drags(macroscopic motion). On heating the same puddle gradually, at a certain temperature, slight currents will develop(convection) which spreads the heat uniformly to the puddle. If you heat it further, at higher temperature, the system becomes CHAOTIC, having sufficiently more energy to overcome viscous drags and come into motion. Soon enough evaporation starts and then boiling, and after that, there isn't a puddle anymore! 
