Can two galaxies move away from each other faster than the speed of light? 

The short, and possibly surprising, answer to this question is yes.

The Hubble constant is the measure of how fast the Universe is expanding today and its value has been measured to be 70 km/s per Megaparsec (a parsec is just a unit of distance equal to about 3.26 light-years, and a Megaparsec is a million parsecs). This means that on average, for every Megaparsec two galaxies are separated by, they are moving away from each other by 70 km/s. Therefore, to be moving away from each other at the speed of light, two galaxies would need to be separated by a distance of about 4,300 billion parsecs. This is smaller than the radius of the observable Universe, therefore not only are there galaxies in the Universe that are moving away from us faster than light, but we can still see them!

This raises two additional questions:

1. If another galaxy is moving away from us faster than light, how can we still see it?
2. Isn't it a violation of the theory of relativity to have two things moving apart faster than the speed of light?

The answer to the first of these questions is that the light the distant galaxy is emitting today will never reach us, so we will never know what it looks like today. This is because today it is moving away from us faster than light, so the light it emits doesn't travel fast enough to ever reach us. However, the light that it emitted billions of years ago, when the Universe was smaller (remember it has been expanding all along) and when that galaxy wasn't receding from the Milky Way as fast, is what we are seeing today. In other words, we are seeing that galaxy as it was billions of years ago.
The second question is an interesting one that confuses many people. The theory of relativity does indeed state that nothing can travel faster than light, however this refers to motion in the traditional sense, meaning you can't launch a spaceship and travel through space faster than light. The two galaxies we've been discussing are not travelling through space, it is the space between them that is expanding. Or put in another way, they are stationary and all the space around them is being stretched out. This is why it doesn't violate the theory of relativity, because it is not motion in the traditional sense.

Source:curious.astro.cornell.edu