It has been discovered that several very different surfaces exhibit a common property: unusually large vibration amplitudes of the outermost atoms, well beyond the enhancement normally expected at typical clean surfaces. These special surfaces are ice H2O(0001), alpha-Al2O3(0001), alpha-Ga(010), and Si(111)-(2 x 1). The root-mean-square vibration amplitudes in these surfaces are at least double the bulk values. The common cause that may explain these vibration amplitudes is that the surface atoms (or molecules in the case of ice) only have back-bonds that are nearly parallel to the surface. In this geometry, vibrations, especially perpendicular to the surface, involve primarily bond bending rather than bond stretching/compression: since bond bending is relatively soft, the corresponding vibration modes can have larger amplitudes. It is suggested that theory examine and confirm this cause of enhanced surface vibration amplitudes and explore its implications for other phenomena such as adsorption and catalysis.