There is a point at which Earth's atmosphere is so thin and gravity is so weak that a person or object at that altitude would not fall to Earth, but would rather just slowly orbit Earth. This is approximately 100 kilometers, or about 62 miles, above the Earth's surface. This is also where "outer space" is said to begin.
Actually, there's no exact altitude at which the earth's gravity loses effect. The pull of Earth's gravity tapers off so slowly and gradually that it's impossible to say where it ends. It technically extends infinitely, but gets weaker and weaker the further out you go. This is because everything in the Universe has a gravitational pull on everything else in the Universe.
So while Earth's gravity truly never ends, at about 62 miles above sea level, someone who jumped out of a plane or spacecraft would simply appear to float in the air like an astronaut in space.
Furthermore, while Earth's gravity extends indefinitely, there's a point at which the gravity of the moon would be dominant and pull a person toward the moon. Beyond the moon, the sun's gravity would take over and cause the person or object to orbit the Sun.
Discover 20 Things You Didn't Know About... Gravity featured at DiscoverMagazine.com.