We analyze the structure diagram for binary clusters of Lennard-Jones particles by means of a global optimization approach for a large range of cluster sizes, compositions, and interaction energies and present a publicly accessible database of 180 000 minimal energy structures (http://softmattertheory.lu/clusters.html). We identify a variety of structures such as core-shell clusters, Janus clusters, and clusters in which the minority species is located at the vertices of icosahedra. Such clusters can be synthesized from nanoparticles in agglomeration experiments and used as building blocks in colloidal molecules or crystals. We discuss the factors that determine the formation of clusters with specific structures.