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In this work, we present NENCI-2021, a benchmark database of approximately 8,000 non-equilibrium non-covalent interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases, and extends the scope of these works by:(i) including 40 cation-and anion-\pi complexes, a fundamentally important class of non-covalent interactions (NCIs) that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PES) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7\times\mathrm {-} 1.1\times the equilibrium separation) as well as nine intermolecular angles per distance (five for each ion-\pi complex), yielding an extensive database of 7,763 benchmark intermolecular interaction energies (E_ {\rm int}) obtained at the CCSD (T)/CBS level of theory. In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent--these interactions in particular pose an enormous challenge for molecular modeling and are observed in many important …