Marine cyanobacteria are considered a prolific source of bioactive natural products with a range of biotechnological and pharmacological applications. However, data on the production of natural compounds from sponge-associated cyanobacteria are scarce. This study aimed to assess the potential of sponge-associated cyanobacteria strains representing different taxonomic groups for the production of bioactive compounds and the biological activity of their extracts. Phylogenetic analysis of sponge-associated cyanobacteria and screening for the presence of genes encoding non-ribosomal peptide synthetases (NRPSs) and polyketide synthases (PKSs) were performed. Methanol extracts of the sponge-associated strains were analyzed for cyanotoxin production and tested for antioxidant activity and cytotoxic activity against several human cancer cell lines and pathogenic bacteria. PKS were detected in all sponge-associated strains examined, indicating the metabolic potential of the isolates. PKS genes were more ubiquitous than NRPS genes. Cyanotoxins (i.e., cylindrospermopsin, anatoxin-a, nodularin, and microcystins) were not detected in any of the sponge-associated cyanobacterial strains. Strains belonging to Leptothoe, Pseudanabaena, and Synechococcus were found to have activity mainly against Staphylococcus aureus. In addition, sponge-associated Leptothoe strains (TAU-MAC 0915, 1015, 1115, and 1215) were found to be highly cytotoxic and in most cases more effective against human cancer cell lines than against normal cells. Extracts with the most promising bioactivity deserve further investigation in order to isolate and identify the bioactive molecule(s).