With the advent of intense, coherent light sources in the XUV and soft X-ray regime, X-ray Thomson scattering becomes a unique tool for the diagnostics of dense plasmas. The scattering spectrum gives direct access to plasma properties like density, temperature, and composition. In dense systems, collisions among constituents are of primary importance for the prediction and interpretation of the scattering signal. We present a systematic approach to the dynamical structure factor using the Born-Mermin ansatz to include collisions via the dynamical collision frequency. Calculations of the scattering spectrum are performed for X-ray scattering on solid and compressed beryllium targets as well as for XUV-photons scattering on hydrogen at near solid density.