Jude 1:6 And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day.
These are the Angels believed to have cohabitated with humans in the OT. One could argue this single verse out as simply as interjection by the Author. However, Jude and Paul both made mention of this event in Gen 6. Paul mention this in 1 Cor 11:10 For this cause ought the woman to have power on her head because of the angels. This is a pretty cryptic verse, but in light of this subject it seems to fit very well.
There are two schools of thought when it come to Angels cohabitating with humans(a)Angels can not produce offspring through physical copulation (b)they can, or a least through some means of DNA manipulation.
It's all pretty interesting to study, for me at least, it answered some of the questions I had about Greek Mythology. As some of the posters have mentioned here, ancient peoples relied on stories and traditions (ie: Greeks).
It is my belief, Satan knew where his downfall would come through (the seed of the woman Gen 3:16), it would therefore seem reasonable that he would try to pollute the human bloodline to keep that from happening. He did this in Gen 6 and even after that. Remember, Joshua, Caleb and David had to complete killing these Giant remnants off. In some cases Israel was not even allowed to keep the spoils, like animals, it seems they were corrupted too. God supernaturally intervened to make this happen.
I often hear people saying, If God is so good, how could he command Israel to kill everything and everyone in these enemy camps? Simple to protect the human blood line so the Christ could be born from the seed of the woman, namely Mary.
Now I know this may seem controversial, but, it was the Holy Spirit that overshadowed Mary and she became with child (The Holy One of Israel, Jesus). Since Satan (and these Angels)has supernatural power, could they possibly have had the same power to corrupt the human seed in Gen Chapter 6? If Jude is any indication of Angels positions (estates), they seem to have left what they knew was right to do something very wrong. They paid the price, but not before much human suffering.
Sorry for the long post, there is just so much on this subject. If you are indeed interested in this subject, posters have listed some great links here, again, Eat the Meat and Leave the Bone, protect yourself with prayer.
God Bless