Drug repositioning applies established drugs to new disease indications with increasing success. A pre-requisite for drug repurposing is drug promiscuity (polypharmacology) - a drug's ability to bind to several targets. There is a long standing debate on the reasons for drug promiscuity. Based on large compound screens, hydrophobicity and molecular weight have been suggested as key reasons. However, the results are sometimes contradictory and leave space for further analysis. Protein structures offer a structural dimension to explain promiscuity: Can a drug bind multiple targets because the drug is flexible or because the targets are structurally similar or even share similar binding sites? We present a systematic study of drug promiscuity based on structural data of PDB target proteins with a set of 164 promiscuous drugs. We show that there is no correlation between the degree of promiscuity and ligand properties such as hydrophobicity or molecular weight but a weak correlation to conformational flexibility. However, we do find a correlation between promiscuity and structural similarity as well as binding site similarity of protein targets. In particular, 71% of the drugs have at least two targets with similar binding sites. In order to overcome issues in detection of remotely similar binding sites, we employed a score for binding site similarity: LigandRMSD measures the similarity of the aligned ligands and uncovers remote local similarities in proteins. It can be applied to arbitrary structural binding site alignments. Three representative examples, namely the anti-cancer drug methotrexate, the natural product quercetin and the anti-diabetic drug acarbose are discussed in detail. Our findings suggest that global structural and binding site similarity play a more important role to explain the observed drug promiscuity in the PDB than physicochemical drug properties like hydrophobicity or molecular weight. Additionally, we find ligand flexibility to have a minor influence.