According to Newtonian mechanics, F=ma, where F is the force of gravity
(no air resistance here), and a is the acceleration, and m is the mass
of the object. For gravity, F=mg, where g is the gravitational
acceleration, giving a=g. If the object doesn't hit something first, it
will continue to accelerate.
Something falling in towards Earth will have a speed of at least
the escape velocity of the Earth, about 25,000 miles per hour. The
Earth's gravitational field is not uniform -- it gets weaker the
farther out you go. Also, objects such as meteors can have some
additional energy due to their motion before they got near the Earth.
There is a speed limit to everything, though, and that's the speed
of light; nothing goes faster, not even things that have been falling
in a gravitational field for a long time.
Long before that speed limit is approached, air resistance will
keep falling objects from exceeding a "terminal velocity" -- that speed
when the force of air resistance exactly cancels out the downward pull
(published on 10/22/2007)