That depends on how high up you start from, and the mass of the object that you're dropping.
Acceleration due to gravity:
where G is Newton's gravitational constant,
is the mass of the earth and r is the distance to the center of the earth. In as much as the radius of the earth is very large compared to laboratory dimensions, an object near the surface of the earth, r is approximately constant and equal to the radius of the earth,
It's possible to experience constant acceleration, if you're "near" the surface of the earth, or the relative mass is "insignificant."