How far from the end of Earth's atmosphere does the planet's gravitational field extend?

The inverse square law clearly shows, mathematically, that there is no distance where gravitational interaction is equal to zero. So, in a static universe, the answer is 'infinite.'

But there are two other things you might want to consider.

1. At the common center of mass between two bodies, their gravity cancels each other out. You could argue just as easily that both are affecting you or that neither is as a result of being in this location. You might also want to assume that a certain gravitational acceleration is negligible. A star 500 light years away from you have basically no gravitational effect on you, at least not in your lifetime.

2. The universe is not static, and gravity (as far as we know) propagates at light speed. So, objects beyond our observable horizon, can never affect us directly through their gravity, since not only their light will never reach us, but their gravity as well.

While it is true that the gravitational influence of any object extends out to infinity in an inverse-square fashion, in practical terms the object's Hill sphere (or Roche sphere if you prefer) gives the approximate bounds of its gravitational dominance in relation to other major bodies.

http://en.wikipedia.org/wiki/Hill_sphere

In the case of the Earth, the Hill sphere extends out about 1.5 million km from the planet.

Infinity!

It depends on how sensitve yourmeasurments are. Inverse square law.