The First Doctor falsely claimed that the TARDIS' fluid link had run out of mercury as a ruse to explore the Dalek City. The link was later confiscated by the Daleks and accidentally left behind in the city, forcing the time travellers to help the Thals fight the Daleks to recover it. (TV: The Daleks) While the TARDIS was being brought to the Animus by the Zarbi, Vicki accidentally re-aligned the fluid link, which restored power to the ship. (TV: The Web Planet)
A malfunction caused the fluid links to explode, filling the TARDIS with mercury fumes and forcing the Second Doctor and Jamie McCrimmon to evacuate the TARDIS. (TV: The Wheel in Space) The fluid links overheated again when the TARDIS was caught in a volcanic eruption on Dulkis. The Doctor was forced to take the TARDIS out of reality itself. (TV: The Mind Robber) When trying to navigate the rings of Saturn, the Doctor was afraid the fluid links would become damaged. (PROSE: The Wheel of Ice)
The Fourth Doctor and Sarah Jane Smith rescued a ship from a pirate fleet of Grakinese Corsairs by exchanging with them some mercury from a fluid link. They got some more mercury in 1931 Chicago, unknowingly defeating the Master's plans in doing so. (PROSE: The Duke of Dominoes)
Behind the scenes
The BBC concept art for River Song's sonic screwdriver depict a small tubular attachment listed as a "fluid link" along one side of the device, leading up to a section with a blue button, referred to as a TARDIS recall button.