Exact calculation of the van der Waals interaction between closely spaced plasmonic nanoparticles is challenging due to the strong concentration of the electromagnetic fields that takes place at the nanometric gap between them. The technique of transformation optics, capable of mapping a small volume into any desired length scale, enables us to shed physical insight into the intricate behavior of electromagnetic fields in extremely small gaps. Using this theoretical tool, we obtain universal analytical expressions for the van der Waals interactions between spherical nanoparticles made of realistic metals at arbitrary separation.