After much debate, I am finally confident enough to start mocking all those idiots that disagree with my (recently established) position on Genesis six: the Nephilim.
To get the Hebrew out of the way: נפל is the root word used here, and it means to fall (nephel). The plural ending is added, and the root word expanded, until it becomes נפילימ, nephilim, simply "fallen ones," as in rebels or apostates. Which doesn't really help us at all.
Here, I am going to outline the problems with both theories and the answers to them (where applicable), starting with the most commonly held: that the Godly line of Seth is intermarrying with the ungodly line of Cain.
First off, the phrasing is quite odd: "the sons of God... the daughters of men..." Sons of God is used elsewhere, though it's not exactly common, and it usually means the godly humans. Granted, and gladly. The issue is with its combination with "daughters of men," which is almost never used elsewhere in Scripture, and how that leaves all the masculinity on one side.
The implication is that the men of the line of Seth saw the daughters of Cain, and married them, while the daughters of the line of Seth did no such thing, which is problematic. The only plausible explanation I have heard is that the text is attempting to demonstrate the abdication of the Godly men, and demonstrates the effects of the Godly pursuing the ungodly, perhaps as a warning to future readers. While plausible, this argument is demonstrably weak, and rather difficult to extract from the plain text. Let us leave it as a possibility, and move on to the second and greater problem: giants.
The implication of the text here gives us a bit of an issue for the line of Seth theory. The sons of God (Christians) married the lovely daughters of men (the non unattractive pagan mall rats) and had kids. The kids were giants; great heroes, revered men. Why? There is no plausible explanation for why the marriage of a Christian with a pagan results in a giant--not a single one--and there are unlimited examples to the contrary, down to the present day. The only way out of it is to try to dissociate the giants from the marriages, which fails: see Genesis 6:1 and 6:4, and compare: "Now it came to pass... In those days." What days? The giants began in those days, when the sons of God saw the daughters of men.
Taking these two together, the violence done to the text to explain away the first problem is by no means justified when we are left with such a massive problem in the theory we are trying to salvage.
On to the problems with the second theory: the sons of God are angels.
First off, angels are spiritual beings, humans are physical. How can there be attraction between them?
A couple of points: there is the 1 Corinthians 11:6-10 verse, which I'm not even going to mention here. It at least links angels and women in a suggestive way, though it tells us nothing. Also, we are exposing our ridiculous dualism here: our underlying assumption is that the spiritual and physical are totally separated. Finally, we are assuming that angels are spiritual, which, oddly enough, we have no reason to do. We are told that we host angels (Hebrews 13:2), and angels do all sorts of non-spiritual things (like eat food and slaughter people). So it is quite likely that they are either both physical and spiritual (like us), or that they can at least act like it.
Secondly, it just seems crazy.
Personally, I'd like to list this under the arguments for it being correct, and here's my rather complicated logic: 1. We are stupid and usually wrong (see the Bible).
Third: the text is focused on men, their sins, and God's response.
This seems to be the most difficult problem, but let us examine it closer. God's response to the intermarriage is to say, in essence, "Okay, that's it. I've had enough." ("I will not strive with man forever...") Also, keep in mind that it is the descendants that are primarily focused upon. Both of these fit quite well within the theory that the Sons of God are angels. Overall, the text allows for the angel theory quite easily: "man is extremely sinful, and now he is getting an influx of supernatural blood, magnifying him in every way, so that's it; I'm done with him, on to Noah."
The final problem is a problem for both theories: the nephilim (נפילימ) exist after the fall.
There are three possible explanations, and none of them involve holding their breath (for these I'm indebted to Doug Wilson).
First, the same thing might have happened again. Second, the dna for these fallen ones might have been preserved through the line of Noah (very unlikely, given the text of Genesis 6: nephilim=bad, therefore I'm going to destroy the world except one family, which will of course preserve the nephilim). The most likely theory is simply that the name was later applied to non-nephilim giants, and the appellation was what survived the flood.
Given all of these, I've got to go with the theory of the Sons of God being the angels spoken of in Jude 6 and 1 Peter 3:19-20 (time of Noah is in particular illuminating in verse 20).
Any theories, arguments I failed to mention, or any type of problem that any of you have with this, please comment.