"Muggle fireplaces aren't supposed to be connected, strictly speaking — but I've got a useful contact at the Floo Regulation Panel and he fixed it for me. I can put it right in a jiffy, though, don't worry."
-- Mr Weasley to the Dursleys (GF4)
A division of the Department of Magical Transportation with responsibility for Floo Network fireplaces
The Floo Regulation Panel controls which fireplaces are connected to the Floo Network. It is against regulations for a Muggle fireplace to on the Floo Network, although Arthur Weasley manages to have the Dursley's blocked (unbeknownst to him) front room fireplace connected when he and the twins come to pick up Harry (GF4). A simple spell is all that is needed to disconnect a fireplace from the Network (Pm).
Virtually all wizarding homes are connected to the Floo Network. Other connections to the Network exist at wizarding workplaces and the Ministry of Magic, although the fireplaces at Hogwarts are not usually connected. (Pm)