In the last years substantial progress has been made in modelling turbulent clouds and describing their structure by characteristic parameters. The missing link for a systematic comparison between models and observations is the lack of efficient radiative transfer algorithms to generate molecular line maps from the models comparable to the observed maps. A fully self-consistent solution of the radiative transfer problem is computationally very demanding and hardly suited to evaluate a large set of cloud models with regard to their agreement with observed molecular cloud structures. We introduce a new, computationally efficient code to calculate the line profiles based on two reasonable approximations. It is able to compute the molecular line maps in turbulent cloud models with an accuracy of about 20% fast enough to be run on large sets of model clouds. Applying the code to hydrodynamic, and magnetohydrodynamic cloud models we study how their structure would appear in molecular line observations. We show that no single molecular line provides a good measure for the density structure in the models. The X factor, translating the integrated line intensities into column densities, can be approximately constant within a density range covering up to a factor 100 in few transitions but for each line this behaviour breaks down outside of a limited range of densities. Optical depth effects and subthermal excitation result in a significant modification of the distribution of line intensities relative to the column density distribution. All lower transitions of CO isotopes only trace gas at low and intermediate densities which is distributed over all scales in molecular clouds. Turbulence models driven on the largest scales reproduce the observed scaling behaviour. Higher CO transitions are only excited in dense cores resulting from shocks or gravitational collapse. The existence of massive dense cores resulting from collapse can only be inferred when comparing observations in different transitions taken with an excellent signal-to-noise ratio or from dedicated high-density tracers. The line profiles obtained from turbulence models driven on large scales break up into several fragments in contrast to observations of molecular clouds without heavy star-formation which show typically smooth profiles with close-to-Gaussian shape. None of the turbulence simulations provides a good match of all observed properties for this type of clouds. The velocity scaling behaviour of all observations and turbulence models is consistent with the interpretation of a molecular cloud as shock-dominated medium. More observational data are needed to provide a reliable conclusion on the degree of intermittency. As molecular lines fail to reflect the density structure of an interstellar cloud line observations should be combined with dust continuum observations to deduce column densities. On the other hand we need the velocity information contained in line observations to discriminate between different turbulence models.