Anglo-Zanzibar War
Wikipedia's entry on
the shortest war:
The Anglo-Zanzibar War was fought between the United Kingdom and Zanzibar on 27 August 1896. With a duration of only 45 minutes, it holds the record of being the shortest war in recorded history.
The war broke out after Sultan Hamad bin Thuwaini, who had willingly co-operated with the British colonial administration, died on 25 August 1896, and his nephew, Khalid bin Bargash, seized power in what amounted to a coup d'état. The British favoured another candidate, Hamud bin Muhammed, whom they believed it would be easier to work with, and delivered an ultimatum ordering Bargash to abdicate.
(Thanks Jack)