This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
Where to direct vision is critical for fast cornering. Central vision
should be focused on the pavement where the tire will track, while
allowing peripheral vision, with its low resolution and good
sensitivity to motion, to detect obstacles and possible oncoming
traffic. Peripheral vision monitors surroundings anyway, so the
presence of a car in that "backdrop" does not require additional
consideration other than its path.
If central vision is directed at the place where an oncoming vehicle
might appear, its appearance presents a new problem of confrontation,
stopping image processing of the road surface for substantial time.
Because the color or model of car is irrelevant, this job can be left
to peripheral vision in high speed primitive processing, while
concentrating on pavement surface and composition.
When following another bicycle or a car downhill, the same technique
is even more important, because by focusing on the leading vehicle,
pavement and road alignment information is being obscured giving a
tendency to mentally become a passenger of that vehicle. Always look
ahead of the vehicle, observing it only peripherally.
Riders often prefer to keep their head upright in curves, although
leaning the head with the bicycle and body is more natural to the
motion. Pilots who roll their aircraft do not attempt to keep their
head level during the maneuver, or in curves, for that matter.