The basic answer is yes, potentially. To begin, disregard friction, earth rotation, and other problems, and consider the situation of a hole or tunnel entering the earth at one point, traveling straight through its core, and returning to the surface on the other side of the globe. If enough space exists for such a route to be traversable, it can be done. The fact that no one has ever seen or heard of this happening suggests that it does not happen often.
In theory, you could fall into a hole and not be able to get out. That's what happened to Jules Verne's character in his novel "From the Earth to the Moon". He falls into a deep pit on the moon and can't get out. In reality, you would probably be dead before you hit bottom because the moon's gravity isn't strong enough to keep you from falling.
In theory, you could jump off a tower and land in another country. In practice, this usually doesn't work because of legal issues with trade agreements and things like that. However, there have been cases where people have jumped off towers and been rescued by emergency crews who arrived soon after they had jumped.
In theory, you could walk out onto water and fall off the end of the world. In practice, this doesn't happen because the water would just catch you.
Moving the Earth to a larger orbit might be a solution, and it is theoretically doable. This, however, would be impossible for the Earth due to its massive mass in comparison to even the biggest asteroids. Even if you could move a mountain, the asteroid would still have enough momentum to remain in orbit.
The Earth's orbit is not fixed. It changes over time as different forces act on it. The most important force is the gravitational pull of the Sun. When this becomes stronger than the other forces, it causes the Earth to fall into the Sun. This has happened before - about 50 million years ago - and will happen again someday. But can things get worse? Yes, they can! If the Earth loses enough mass, its gravity will no longer be strong enough to keep the Moon in orbit. Then, the moon will begin to fall towards the Earth...and that's not good.
So basically, yes, the Earth can go out of orbit if something bad happens. But it wouldn't be because of anything people did, it would be because of nature's way for objects with more mass than air (like planets) to remove their content (like atoms) until nothing is left. And when that does happen, the Earth will disappear forever.
If you leapt into a shaft that ran all the way through the Earth, you would fall toward the core, but your rate of acceleration would decrease as you drew closer. (You'd continue to travel faster as you got closer to the center, but not at the same pace.) Eventually, you would stop moving altogether because there is no force pulling you back up towards the surface.
This is what keeps us alive: the gravitational force of Earth is strong enough to keep operating even when it isn't being applied to something solid. If it weren't for this effect, we would all die after we hit water because our bodies would be crushed by the pressure before any signal could reach them.
Here on earth, this effect is used for entertainment purposes in roller coasters. The force of gravity works its way down to your body through the seat of your pants and then some more until it reaches the track beneath you. This pushes you forward into the next section of the ride, where you experience another drop in speed due to gravity's effects.
Your heart continues to beat even when you're falling because muscles still have energy stored inside of them. Once you hit about 100 meters (330 feet) from the ground, however, your heart will start to feel the effects of gravity and will need to work harder to pump blood around your body. At this point, you are already going too fast to survive unless you are wearing a pressurized suit.
You would just float, being pushed evenly in all directions by gravity. Having said that, you'd still be going at an unrivaled pace, so you'd breeze right past that fantastic feeling. The process will begin to reverse when you travel through the Earth's core, still speeding at 6 miles per second. Your body will be torn apart and your atoms will spread out across space, forming a new universe.
Nowadays, we know that objects dropped into the Earth's center don't stay there. They are pulled toward the center by the Earth's mass. However, because the force of attraction is very weak, only items with a lot of mass can be pulled in. For example, astronauts aboard the International Space Station have found that it takes about 2 tons of material to create a new mile-deep hole when falling into Earth's gravity.
The Earth is constantly spinning at more than 1,000 miles per hour. So any object thrown out into free space from its surface will quickly leave the area due to friction between the object and air molecules. Objects thrown out into empty space near the planet will follow parabolic paths until they reach resistance from ambient gases or are caught by the force of another meteorite.
If you were to throw a ball up into the air, it would go up for a while and then come back down. But if you were to throw it far enough, it would never return to Earth.
The force of gravity weakens when one descends below the Earth's surface, as in a mine shaft. Your weight and gravitational attraction diminish as you go closer to the core of the Earth.
Yes! As you got closer to the center of the earth, your weight would diminish. Only the section of the Earth closest to the center contributes to your weight. As you approach closer to the center, the gravitational field weakens and your weight lowers because there is less and less of the Earth closer to the center than you are.