Based on the structural and experimental studies of more than 300 insect species from different lineages, we have developed and characterized a bioinspired polymer material with the ability of multiple glue-free bonding and debonding. The material surface is covered with a pattern of microstructures, which resembles the geometry of tenent hairs previously described from the feet of flies, beetles, earwigs and other insects. The tape with such a microstructure pattern demonstrates at least two times higher pull-off force per unit apparent contact area compared to the flat polymer. Additionally, the tape is less sensitive to contamination by dust particles than a commercially available pressure-sensitive adhesive tape. Even if the 'insect tape' is contaminated, it can be washed with a soap solution in water, in order to completely recover its adhesive properties. We have successfully applied the tape to the 120 g wall-climbing robot Mini-Whegs. Furthermore, the tape can be used for multiple adhering of objects to glass surfaces or as a protective tape for sensitive glass surfaces of optical quality. Another area of potential applications is gripping and manipulation of objects with smooth surfaces.