Would it be possible to pull Mars and Earth closer each other? The burden of travelling between Mars and Earth comes from the distance. If the planets were closer, life could spread to Mars more easily, ensuring the survival of the intelligent lifeforms. What would it take to pull the two planets closer each other? How much energy would be required? Would it even be possible to move planets without losing the stability of the orbit? Is this manipulation of orbits possible even in theory? 
To give some numeric data, the average orbit radius of Mars from Sun is about 1.5 times the orbit radius of Earth (1 AU). The distance between Mars and Earth varies from 0.5 AU to 2.5 AU. For reference, the distance between Moon and Earth is about 0.003 AU. The orbital period of Mars is 687 days and Earth 365 days. The mass of Mars is about 0.11 Earths.
 A: I imagine you don't really want to know if it is possible. Yes, given insanely huge amounts of energy, insanely huge jobs are possible. 
You probably want to know if we could do it. And the answer is No. Not a chance. 
Lets start with a job that is microscopic when compared to a planet. Could we move Mt Whitney a hundred miles and partially fill in Death Valley? Mt. Whitney is about 2 miles taller than the Valley floor below it. Let's suppose it is about 2 miles on a side, or 8 cubic miles of rock. 
In 20 years or so, the Egyptians built the Great Pyramid. It is almost 500 feet tall, less that 0.1 miles. So forget hand labor. 
In the modern world, we use power equipment. The Hull Rust open pit mine is one of the biggest in the world. Its maximum dimensions are are about 5 miles x 2 miles x 0.1 miles deep, about 1 cubic mile. It has been open since 1895. Let's give ourselves the benefit of the doubt and say we could do 10 times better. In that case, we could level Mt Whitney in about a century. 
But we couldn't take on a small job like moving a 20 x 20 x 20 mile chunk of rock 1000 miles.
Mars is bigger than a 3000 x 3000 x 3000 mile rock. We would have to move it about 50,000,000 miles to get it to Earth. 
A: Suppose we could accelerate an asteroid to an insane velocity and have it smack into Mars. Let's use Ceres, the most massive asteroid. Mars is almost 700 times as massive as is Ceres. Even a very large smack won't do much. Suppose we could make Ceres smack into Mars at 120 km/s in a purely inelastic collision. If done at Mars aphelion, this could decrease Mars perihelion from 1.38 AU to 1.34 AU -- except for one thing. Mars would no longer exist. I picked 120 km/s because that is more than enough energy to gravitationally unbind Mars.
One smack, even from a large asteroid such as Ceres, will not do it. Somehow making every asteroid in the asteroid belt smack into Mars will not do it; Ceres represents about 30% of the mass of the asteroid belt. Accelerating Ceres to 120 km/s represents about 10 billion years of humankind's total energy consumption, based on 2010 numbers.
A: Often the ability to do something is simply sparked by the knowledge that something is possible. It has been argued that reason why the Germans did not make an atom bomb during the second world war was because they didn't think it was possible.
So, instead of asking: can one move a planet to a different orbit?, let's ask, how would one move a planet to a different orbit? Well, when people started to identify exo-planets, they found that the first one's they saw (due to the way they were identified) are big and close to their stars. So the question came up: how did these planets get so close to the stars. The proposed mechanisms included some migration of the planet from a larger orbit to a smaller one due to the debris lying between the planet and the star. As the debris gets thrown out of the system by the planet, it would gradually migrate closer.
So this suggests a mechanism to migrate a planet. There are asteroids and comets in our solar system that can in principle be used to perform this process. One would have to start with the smallest comets. Steer them into orbits that would pass close to bigger ones, thereby steering them into orbits that would affect still bigger objects; up until one can send them close to the target planet, thus gradually affecting the orbit of the planet.
Granted, this would be an extremely complex and even more extremely long term project, but it is in principle possible.
