Ultraviolet radiation is known to inhibit photosynthesis, induce DNA destruction and cause damage to a wide variety of proteins and lipids. In particular, UV radiation between 200 and 300 nm becomes energetically very damaging to most of the terrestrial biological systems. On the other hand, UV radiation is usually considered one of the most important energy source on the primitive Earth for the synthesis of many biochemical compounds and, therefore, essential for several biogenesis processes. In this work, we use these properties of the UV radiation to define the boundaries of an ultraviolet habitable zone. We also analyze the evolution of the UV habitable zone during the main sequence stage of the star. We apply these criteria to study the UV habitable zone for those extrasolar planetary systems that were observed by the International Ultraviolet Explorer (IUE). We analyze the possibility that extrasolar planets and moons could be suitable for life, according to the UV constrains presented in this work and other accepted criteria of habitability (liquid water, orbital stability, etc.).