The Seventh Doctor first encountered the Foreign Hazard Duty on the planet Mekrom, on the edge of known space. Commander Hurd's FHD team were sent to rescue the inhabitants of a human colony there, but all appeared to have been killed by Mogor. The Doctor revealed that these were ghosts, and the deaths were from shock, rather than a living enemy. (COMIC: Echoes of the Mogor)
An FHD team under Commander Lumsden attempted to stop a species of bookworm from eating their way through the library planet Catalog. The Doctor helped them out, revealing the creatures to be primordial entities. (COMIC: Hunger from the Ends of Time)
An FHD team under Captain Geoff Monmouth was sent to guard important ruins on Aleph 777 from the Sontarans. As the Sontarans were sent to guard it from the humans, both sides were caught in a violent stalemate. (COMIC: Conflict of Interests)
Behind the scenes
The original FHD were clearly inspired by the Colonial Marines from Aliens, with the first team seen sharing names and visuals with characters from Alien and Aliens.
The FHD were created and written exclusively by Dan Abnett. He has stated that he always intended for them to be a future version of UNIT, and that the name was based on slang he used at college: "An FHD was a really good night out, because one got so drunk, one had a terrible hangover in the morning, otherwise known as a F****** Horrible Death. Obviously, for DWM purposes, I changed what it stood for!"