We aim to better understand how the spatial structure of molecular clouds is governed by turbulence. For that, we study the large-scale spatial distribution of low density molecular gas and search for characteristic length scales. We employ a 35 square degrees 13CO 1-0 molecular line survey of Cygnus X and visual extinction (Av) maps of 17 Galactic clouds to analyse the spatial structure using the Delta-variance method. The Delta-variance spectra obtained from the Av maps show differences between low-mass star forming (SF) clouds and massive giant molecular clouds (GMC) in terms of shape of the spectrum and values of the slope beta. Low-mass SF clouds have a double-peak structure with characteristic size scales around 1 pc and 4 pc. These scales may represent SF molecular clumps (1 pc) and/or the width (1 pc) and length (4 pc) of filaments. GMCs show no characteristic scale in the Av-maps which can partly be ascribed to a distance effect due to a larger line-of-sight (LOS) confusion. The Delta-variance for Cygnus, determined from the 13CO survey, shows characteristic scales at 4 pc and 40 pc, either reflecting the filament structure and large-scale turbulence forcing or -- for the 4 pc scale -- the treshhold scale when the 13CO 1-0 line becomes optically thick. Though there are different reasons for characteristic scales (geometry, decaying turbulence, LOS-effects and energy injection due to expanding supernava shells, outflows, etc.), and the relative conribution of these effects strongly varies from cloud to cloud, it is remarkable that the resulting turbulent structure of molecular clouds shows similar characteristics.