The Tribbles from Star Trek remind me of the Mogwai from Gremlins. These cute, furry little creatures both seem harmless at first glance, but each have the amazing ability to rapidly reproduce and multiple asexually causing mischief and devastion everywhere. You'll have to visit and haggle a bit in Chinatown if you're looking for a Mogwai, but you can easily get a Star Trek Interactive Tribble from the 23 century.
Unlike the original "born pregnant" Tribbles, sold by the trader Cyrano Jones, these Tribbles are genetically altered to be sterile and feed on batteries rather than Quadrotriticale grain. These adorable little black, brown and grey fuzzballs come in various sizes, shake and quail when disturbed and are guaranteed to have a calming effect on the nervous systems of most humanoids. Just keep them away from Klingons and whatever you do, don't get them wet or feed them after midnight... or something.