Single-layer MoS2 is a newly emerging two-dimensional semiconductor with a potentially wide range of applications in the fields of nanoelectronics and energy harvesting. The fact that it can be exfoliated down to single-layer thickness, makes MoS2 interesting both for practical applications and for fundamental research, where the structure and crystalline order of ultrathin MoS2 will have a strong influence on electronic, mechanical and other properties. Here, we report on the transmission electron microscopy study of suspended single and few-layer MoS2 membranes with thicknesses previously determined using both optical identification and atomic force microscopy. Electron microscopy shows that monolayer MoS2 displays long-range crystalline order although surface roughening has been observed with ripples which can reach 1 nm in height, just as in the case of graphene, implying that similar mechanisms are responsible for the stability of both 2D materials. The observed ripples could also explain the degradation of mobility in MoS2 due to exfoliation. We also find that symmetry breaking due to the reduction of the number of layers results in distinctive features in electron-beam diffraction patterns of single and multilayer MoS2 which could be used as a method for identifying single layers using only electron microscopy. The isolation of suspended single-layer MoS2 membranes will improve our understanding of two-dimensional systems, their stability and the interplay between their structures, morphologies, electrical and mechanical properties.