Resistance of bacteria, fungi and cancer cells to antibiotics and other drugs is recognized as one of the major problems in current medicine. Therefore, a search for new biologically active compounds able to either kill pathogenic cells or inhibit their growth is mandatory. Hard-to-reach habitats appear to be unexplored sources of microorganisms producing previously unknown antibiotics and other molecules revealing potentially therapeutic properties. Caves belong to such habitats, and Actinobacteria are a predominant group of microorganisms occurring there. This group of bacteria are known for production of many antibiotics and other bioactive compounds. Interestingly, it was demonstrated previously that infection with bacteriophages might enhance production of antibiotics by them. Here, we describe a series of newly isolated strains of Actinobacteria that were found in caves from the Tatra Mountains (Poland). Phage induction tests indicated that some of them may bear active prophages able to produce virions upon treatment with mitomycin C or UV irradiation. Among all the examined bacteria, two newly isolated Streptomyces sp. strains were further characterized to demonstrate their ability to inhibit the growth of pathogenic bacteria (strains of Staphylococcus aureus, Salmonella enterica, Enterococcus sp., Escherichia coli, and Pseudomonas aeruginosa) and fungi (different species and strains from the genus Candida). Moreover, extracts from these Streptomyces strains reduced viability of the breast-cancer cell line T47D. Chemical analyses of these extracts indicated the presence of isomers of dichloranthrabenzoxocinone and 4,10- or 10,12-dichloro-3-O-methylanthrabenzoxocinone, which are putative antimicrobial compounds. Moreover, various previously unknown (unclassified) molecules were also detected using liquid chromatography–mass spectrometry, suggesting that tested Streptomyces strains may synthesize a battery of bioactive compounds with antibacterial, antifungal, and anticancer activities. These results indicate that further studies on the newly isolated Actinobacteria might be a promising approach to develop novel antibacterial, antifungal, and/or anticancer drugs.