As the crow flies
In a direct line, without any of the detours caused by following a road.
The allusion in this expression is obviously to the ability of crows to fly directly from A to B, without the encumbrances of roads and landscape features that restrict man. Crows are perhaps an odd choice as, unlike many birds that migrate over long distances, their flight isn't especially straight. Crows normally fly in large wheeling arcs, looking for food.
The earliest known citation of the phrase, which explicitly defines its meaning, comes in The London Review Of English And Foreign Liturature, by W. Kenrick - 1767:
The Spaniaad [sic], if on foot, always travels as the crow flies, which the openness and dryness of the country permits; neither rivers nor the steepest mountains stop his course, he swims over the one and scales the other.
The term 'the crow road' has long been used in Scotland to denote the most direct route. It has also been used there latterly to indicate death, which is the meaning alluded to in Iain Banks' 1992 eponymous novel. This term is contemporary with 'as the crow flies' and is cited in the 1795 Statistical Account of Scotland, where a turnpike, or 'crow road', was suggested as a means of reducing the costs of road maintenance, by eliminating numerous winding roads:
One of which improvements is evident to the most careless observer; viz. in cutting a line of road from Campsie kirk to the Crow road.