"....it's more than our life's worth to set up an unauthorised Portkey."
-- Remus Lupin to Harry Potter (OP3)
A division of the Department of Magical Transportation with responsibility for Portkey registration and use
The Portkey Office is located on Level Six of the Ministry of Magic headquarters (OP7).
- Basil, who wore a kilt and a poncho at the 1994 Quidditch World Cup (GF7), and
- his colleague at the Portkey landing site, a Ministry wizard wearing a tweed suit and thigh-high galoshes, who had a large gold watch (GF7).
Portkeys have to be authorized (OP3, OP36); this is presumably the Office in charge of that. Since Portkeys are ordinarily made from objects that can pass as litter - objects that might appear on the Registry of Proscribed Charmable Objects, in other words, and which the Muggle Artifacts Office would have to worry about - it's not surprising that the Portkey Office keeps track of them.
It is an essential method of travel for wizards unable to Apparate or where no fireplace exists to allow the use of Floo Powder. The unpleasant side effects of using Portkey travel, however, can include faintness, nausea and vomiting (Pm).
Two Muggles picked up a Portkey on Clapham Common and ended up at a Celestina Warbeck concert (Pm).
from Pottermore: The name ‘Portkey’ comes from the French ‘porter’ - to carry - and the word ‘key’, in the sense of secret or trick.
J K Rowling says she has a real Portkey: the key to the US city of LaPorte, which was given to her by Emerson Spartz of Mugglenet.com (Pm).