An extinguishing spell is a spell which is used to put out fires. Charles Weasley told Rubeus Hagrid that he and his fellow dragon keepers were prepared to cast extinguishing spells should something go wrong during the first task of the Triwizard Tournament. 
When Cho Chang accidentally set Marietta Edgecombe's sleeve on fire by incorrectly pronouncing the incantation of the Disarming Charm, Marietta put the fire out with her wand, presumably using an extinguishing spell.
- Harry Potter and the Goblet of Fire (Mentioned only)
- Harry Potter and the Order of the Phoenix (Possibly)