Rigid hydrocarbon scaffolds play an increasingly important role in modern medicinal chemistry by enabling precise control over molecular geometry, lipophilicity, and target interactions. Adamantane and cubane represent two paradigmatic rigid frameworks with distinct structural and physicochemical characteristics that are highly relevant to computer-aided drug design. Adamantane is a low-strain diamondoid scaffold extensively employed in clinically approved drugs, whereas cubane is a highly strained cubic hydrocarbon that serves as a three-dimensional bioisostere of benzene and offers unique opportunities for molecular innovation. This review provides a comparative analysis of natural adamantane-containing metabolites, synthetic adamantane derivatives, and fully synthetic cubane-based compounds, with a particular focus on computer-aided prediction of biological activity and structure–activity relationships. While adamantane derivatives are well established in antiviral and neuroactive therapeutics, naturally occurring adamantane-type metabolites isolated from plants, marine organisms, and microorganisms display a broad spectrum of biological activities, including anticancer, antiviral, anti-inflammatory, neuroprotective, and cytotoxic effects. In contrast, cubane derivatives—absent from natural biosynthetic pathways—have emerged as promising synthetic pharmacophores enabled by advances in molecular synthesis and in silico screening. The biological potential of structurally diverse adamantane and cubane derivatives bearing amino, nitro, hydroxy, hydroperoxy, halogen, thiol, sulfate, phosphate, and phosphonate functionalities was systematically evaluated using the PASS (Prediction of Activity Spectra for Substances) platform. PASS-guided analysis revealed both complementary and scaffold-specific activity profiles. Aminoadamantanes, including clinically used compounds, showed strong predicted neuroprotective and antiparkinsonian activities, consistent with experimental and clinical data. Notably, phosphonate derivatives of both adamantane and cubane exhibited exceptionally high predicted antiparkinsonian activity, in several cases exceeding that of reference drugs. Selected hydroperoxy and halogenated cubane derivatives demonstrated pronounced predicted antiprotozoal, anti-inflammatory, psychotropic, and antidiabetic activities. Overall, this review highlights the value of rigid hydrocarbon scaffolds combined with computer-aided activity prediction as a strategy for identifying high-priority lead compounds. The results underscore the underexplored pharmacological potential of cubane-based phosphonates and peroxides alongside established adamantane pharmacophores, supporting their further development in neurodegenerative, infectious, and oncological drug discovery.