Viruses can be classified into archaeoviruses, bacterioviruses, and eukaryoviruses according to the taxonomy of the infected host. The host-constrained perception of viruses implies preference of genetic exchange between viruses and cellular organisms of their host superkingdoms and viral origins from host cells either via escape or reduction. However, viruses frequently establish non-lytic interactions with organisms and endogenize into the genomes of bacterial endosymbionts that reside in eukaryotic cells. Such interactions create opportunities for genetic exchange between viruses and organisms of non-host superkingdoms. Here, we take an atypical approach to revisit virus-cell interactions by first identifying protein fold structures in the proteomes of archaeoviruses, bacterioviruses, and eukaryoviruses and second by tracing their spread in the proteomes of superkingdoms Archaea, Bacteria, and Eukarya. The exercise quantified protein structural homologies between viruses and organisms of their host and non-host superkingdoms and revealed likely candidates for virus-to-cell and cell-to-virus gene transfers. Unexpected lifestyle-driven genetic affiliations between bacterioviruses and Eukarya and eukaryoviruses and Bacteria were also predicted in addition to a large cohort of protein folds that were universally shared by viral and cellular proteomes and virus-specific protein folds not detected in cellular proteomes. These protein folds provide unique insights into viral origins and evolution that are generally difficult to recover with traditional sequence alignment-dependent evolutionary analyses owing to the fast mutation rates of viral gene sequences.