A limerick was a rhyming poem or a humorous song, often associated with the Irish on Earth.
After being transported back in time from 2381 to 2259, Ensign Brad Boimler wrote a limerick with which to apologize to the USS Enterprise senior staff for harboring unrealistic expectations of them from the future. Lieutenant Commander Una Chin-Riley stopped him from performing it. (SNW: "Those Old Scientists")
While under the influence of the polywater intoxication in 2364, an officer aboard the USS Enterprise-D delivered a peculiar limerick about a woman from Venus while in the shuttlecraft bay. Data began to quote from it, but was mercifully interrupted by Jean-Luc Picard. (TNG: "The Naked Now") In 2402, Data was asked to give a toast and he began to repeat that particular limerick before being shut down by all his friends. Data responded that he had always wanted to finish that particular limerick. (PIC: "The Last Generation")
Michael Sullivan, while discussed the topic of poetry with Kathryn Janeway, noted how much Jane Eldon and Sean Gogerty shared similar rhyming schemes. Janeway was, however, not familiar with either poet, and was told by Sullivan that she had some catching up to do, and invited her to join him sometime. Sullivan further explained the one time he tried talking poetry with Seamus, but that "all he can do is recite limericks." (VOY: "Fair Haven")
In 2376, Harry Kim considered tweaking Tuvok's holo-program of the Temple of T'Panit, so that instead of Vulcan prayers, the monks recite Ferengi limericks, in attempt to make Tuvok laugh. He shared this thought with Lyndsay Ballard, but her mind was elsewhere. (VOY: "Ashes to Ashes")