We show, both experimentally and theoretically, that the free surface of an elastic bilayer becomes spontaneously rough when brought in contact with another rigid surface. The lateral length scales of these self-organized structures were found to scale as: lambda = R(F)h, where h is the total bilayer thickness. The scale factor, R-F could be modulated by the ratios of the individual film thicknesses and shear moduli. This is unlike the case of a single elastic film where the scale factor is independent of all material properties, RF similar to 3. A linear stability analysis shows that the instability patterns in the bilayer can be tuned from the short waves (similar to 0.5 h) to long waves (similar to 8 h). Experiments show good agreement with the theoretical predictions regarding the existence of short wave deformations. Further, a rather catastrophic change in the wavelength from its minimum value, similar to h/2, to a limiting value of similar to 3 h occurs by very small changes in the film thicknesses. This effect is explained by a switching of states in the bilayer energy curve which displays two minima at different wave numbers. Thus, the contact instability of elastic bilayers suggests novel strategies for the control of adhesion and engineering of feature sizes in a wide range. In particular, these findings have implications for further pattern miniaturization in the elastic contact lithography using pre-patterned stamps.