In the opening scene of Prometheus, do we know why the alien eats the thing that kills him?
The alien looks at his spaceship and then eats the thing that modifies his DNA after killing him.
At this time, no.
There has been a lot of discussion and speculation regarding whether the scene was a depiction of an engineer seeding life on the planet - or initiating the destruction of life by introducing the alien/xenomorph DNA.
The bonus materials on the DVD/Blu-Ray may shed some more insight into this, but I believe it was intentionally vague.
The Lone Engineer at the beginning of Prometheus drank the black liquid in order to seed Earth with intelligent life. This is described on the Prometheus Blu-Ray's extras section, in the caption for one of the deleted scenes:
Scene 7: Arrival of the Engineers
The Engineers touch down on prehistoric Earth for a sacred ritual devoted to the seeding of Intelligent life. Whereas the Theatrical version of the scene is devoted to the Lone Sacrifice Engineer, this early cut features several of his comrades, including the Elder Engineer. The ceremony was filmed with dialogue but unsatisfied with the result, Ridley Scott removed the dialogue entirely.
He was definitely seeding life. This has been stated clearly by Ridley himself and is quite obvious given that the planet appears to be in its formative stages with only minimal plant life.
A pre-vis on the blu-ray actually shows a very primitive amphibian creature crawl out of the water and onto land after the DNA sequence.
Our oldest ancestor, LOL.
My personal belief is that this is not the black goo, this was probably millions of years ago, and the effects are completely different than those of the black goo. It also looks different.
Another scene on the blu-ray shows Ridley designing the sacrificial goo with various berries and coloured honeycomb mashed into a bowl. If it was the black goo, he would have simply made it black. It's not even black, people.
The only question remaining about Prometheus (originally titled Alien Engineers) is why they would want Xenomorphs. Weapon? Cleansing a planet like a Petri dish?