A puzzling, but compelling film.
One particularly interesting aspect are the brothers Paul and Eli Sunday, both played by Paul Dano. Although the wikipedia entry has since been altered (?), mere days ago it contained a section (4.1, if memory serves) on the Paul / Eli Sunday debate (see, for example, here), one of the most interesting sections of the entry, bizarrely removed by busybody Jim Dunning. The issue is this: are they twin brothers, or a single (schizophrenic?) person?
In favor of the former interpretation is Paul Thomas Anderson's intent - according to the now missing section of the wikipedia article, the decision to cast Eli Sunday with Paul Dano was made after filming had already commenced, and Dano's part as Paul Sunday had already been filmed. Purportedly, a younger actor playing Eli was replaced mid-filming (possibly due to Daniel Day Lewis' intimidating practice of staying perpetually in character). The brothers interpretation is also supported by the script.
However, the two characters never appear in the same scene, and Eli exhibits schizophrenic behavior in other scenes (he is, after all, a revivalist preacher who "casts the devil" out of his sick parishioners). When Daniel Plainview (Lewis) taunts Eli by telling him how much he paid Paul Sunday for information about their farm, giving a falsified amount, he almost seems to be daring Eli / Paul to admit his deceit, to break free from his schizophrenia. (Also, note that Paul questions Lewis on his religion before Eli even comes into the picture.)
The question, though, is not what interpretation we want to give here, but rather, what interpretation are we permitted to give - may we consider the author "dead" even as he walks among us, decrying our attempts at interpretation? Of course, most of you reading this will give the quick and obvious answer - but will you all give the same one?