A recurring problem in science fiction movies is that aliens are often not really alien. Star Trek, for instance, is noted as being about Americans with different things plastered to their forehead.
Sometimes, the aliens are truly different from us, but hostile, such as The Thing, Invasion of the Body Snatchers, and of course, Alien. In this category, though the aliens are completely foreign, both physiologically and psychologically, we get to only experience few aspects, consistent with them being an enemy of war.
District 9 introduces some aliens that really are different from us. They arrive in a huge spaceship hovering mysteriously over Johannesburg. The initial encounter when humans enter the ship is not what you would expect. Spoilers follow.
The aliens, called prawns, looks like they need help, so the South African government interns them all in a shanty-town depressingly reminiscent of Soweto. I have a feeling the parallel was intentional, though apartheid is fortunately never mentioned.
To introduce the situation, some experts are speaking on camera in the beginning of the movie. At first, I thought this was a bad sign. I was not in the mood to watch talking heads for two hours. This only lasts for a bit, until the story starts. The story itself does not break new ground, but it is well told and well acted, and you experience the protagonist bonding with one of the enigmatic aliens, as well as undergoing a transformation of his own, in at least two ways.
Many commenters have questioned the appearent simplicity of the aliens. Maybe they have not thought it through. How would Paul Krugman do in the Soweto ghetto? The prawns are certainly displaying values much different from ours, but that is precisely what makes them alien. For instance, to me it seemed like they valued many things above their own lives, yet, they had the ability to grieve for each other.