The objective of this work was to study the adsorption and separation of the most important families of hydrocarbon compounds on metal-organic frameworks (MOFs), in comparison with zeolites. For this purpose, we have selected four probe molecules, each of them representing one of these families, i.e., o- and p-xylene as aromatics, 1-octene as an alkene, and n-octane as an alkane. The separation of these four molecules was studied by binary breakthrough experiments. To represent the large diversity of MOF structures, the experiments were carried out with (i) two MOFs with coordinatively unsaturated metal sites (CUS), i.e., Cu-btc (HKUST-1) and CPO-27-Ni, (ii) a MOF with an anionic framework and extraframework cations, i.e. RHO-ZMOF, and (iii) two rather apolar zeolitic imidazolate framework (ZIF) materials with different pore sizes, i.e. ZIF-8 and ZIF-76. Zeolite NaY and zeolite β were used as polar and apolar reference adsorbents, respectively. The results can be briefly summarized as follows: ZIFs (not carrying any polar functional groups) behave like apolar adsorbents and exhibit very interesting and unexpected molecular sieving properties. CUS-MOFs behave like polar adsorbents but show the specificity of preferring alkenes over aromatics. This feature is rationalized thanks to DFT+D calculations. MOFs with extraframework cations behave like polar (cationic) zeolites.