Livingston - Picard's fish - Star Trek: The Next Generation
When Star Trek: The Next Generation debuted in 1987, the goal of the show was to distinguish itself visually from the original series. Where the original enterprise was a Spartan and spare vessel for charting an unexplored Alpha Quadrant, the Enterprise-D was a spacebourne cruise ship cum science institute full of diplomats with carpeting on the bridge and a fully stocked bar.
Where Captain Kirk did all his work at his Captain's chair on the bridge, Picard had a well-appointed office, his "ready room," which wouldn't look out of place as the corner office in a high profile law firm. And in one corner, by the full-length windows that showed the stars dramatically whizzing by, there was a tank containing Livingston, an exotic red lionfish.
Livingston's presence not only symbolizes the new 'cruise ship in space' approach but also the way the Enterprise brought a little piece of earthbound comfort into deep space to explore deep space. Whenever Picard had to confer with a mysterious or curious alien entity in his ready room, like Q, or Hugh the self-aware young Borg, they'd inspect Livingston to show their curiosity about humanity.
Livingston was set dressing for the most part and didn't play a huge role in the stories, but in the unfairly maligned horror episode "Genesis," where a virus causes the crew to devolve into primitive creatures, Livingston turned into a jellyfish-type thing, who had to be rescued from a presumably hungry Neanderthalesque Riker trying to break into his tank.