The roughness of solids is crucial for interactions between bodies at short separations due to capillary or van der Waals-Casimir forces and for contact mechanics. Specifically, it is critical for the fabrication and operation of microelectromechanical systems, for which functional materials are deposited using thin film coating technologies. Here, it is demonstrated that the materials deposited by magnetron sputtering or thermally evaporated on a cold Si substrate reveal a significantly larger number of high asperities than that predicted by the normal distribution. Such asperities define the distance between the solids in contact that is the key parameter for many problems. The effect is related to the nonequilibrium deposition conditions and is suppressed if the material is deposited on a hot substrate or annealed. The high asperity tails can be described by the extreme value distribution or in some cases by the exponential distribution.