The Doorpost Cross mat be any form but the Tau or Latin crosses are perhaps the most common.
The Tau is believed to have been used by Hebrew slaves in Egypt to mark their doorposts with the blood from a sacrificed animal so that the angel of death would pass-over1 their families.
Conveniently, 'T' was the first letter of the name of the god Tammuz; the dying and rising god, a deity of life-death-rebirth. During baptism ceremonies, this cross was marked on the foreheads by the pagan priest.
More recently, in the Middle Ages, marking a cross on the doorpost or on the door itself, was a warning to people not to enter. It signified that somebody in the house had died of the pestilence. (See Plague Cross.)
Irish folklore dictates that a cross on the door will protect a house from fire (see St. Brighid's Cross) but since most house fires start within the home (electrical faults or cigarette ash2) a cross on the door is unlikely to be very effective.
Today, hanging a cross on your doorpost is akin to wearing a Lapel pin cross. Before visitors even knock on your door, they assume much about your religious beliefs. (And this should be borne in mind if you think it is just a superstitious decoration like a lucky horseshoe.)
Also, don't assume that a cross on the doorpost will in any way Bless This House; and who needs a house blessed anyway? Blessed occupants should be the primary concern.
Blessing, as you probably know already, comes not from a cross on a doorpost but from the love of God. Protection of life, and here we mean the more important spiritual life rather than just the physical life, also comes from the love of God.
See the real meaning of the cross.