Genesis 6:1-7
1 When men began to increase in number on the earth and daughters were born to them, 2 the sons of God saw that the daughters of men were beautiful, and they married any of them they chose. 3 Then the LORD said, "My Spirit will not contend with man forever, for he is mortal ; his days will be a hundred and twenty years." 4 The Nephilim were on the earth in those days—and also afterward—when the sons of God went to the daughters of men and had children by them. They were the heroes of old, men of renown. 5 The LORD saw how great man's wickedness on the earth had become, and that every inclination of the thoughts of his heart was only evil all the time. 6 The LORD was grieved that he had made man on the earth, and his heart was filled with pain. 7 So the LORD said, "I will wipe mankind, whom I have created, from the face of the earth—men and animals, and creatures that move along the ground, and birds of the air—for I am grieved that I have made them." NIV

The Sons of God

Nobody knows what the ''Sons of God'' were, but the most obvious interpretation is that the Nephilim were a hybrid race between two distinct but sexually compatible beings. Many believe the ''Sons of God'' were fallen angels who corrupted mankind. The ''Sons of God''' are clearly distinguished from the daughters of men. This suggests the ''Sons of God'' were either not born on earth or simply righteous men as opposed to earthly. We can only speculate, but as angels are not biological organisms, they are not likely to be reproductively compatible with humans.

Another logical interpretation for the ''Sons of God'' is they were other created men. It is largely assumed that Adam and Eve were the only humans created in the beginning, but the Bible does not describe every person on earth, nor even everyone that was important to God. Only key individuals or situations are included within the text, and we can not say with certainty that God only created one pair of humans.

The phrase "sons of God" used in Genesis 6 is “bene elohim”, which used apparently only three other times in Scripture and in each of the other cases it is found in the book of Job which is accepted as one of the most ancient books written. Job 1:6; 2:1; 38:7.

Job 1:6 Now there was a day when the sons of God came to present themselves before the LORD, and Satan came also among them.
Job 2:1 Again there was a day when the sons of God came to present themselves before the LORD, and Satan came also among them to present himself before the LORD.
Job 38:7 When the morning stars sang together, and all the sons of God shouted for joy?

And Also Afterward

In Genesis 6:4 it is said the Nephilim were on the Earth in those days - and also afterward. This seems to clearly imply that the Nephilim were also on the Earth after the flood of Noah. Although the Nephilim are only mentioned one other time in scripture after Genesis 6, during a false report brought back to Moses by the explorers of Canaan, this reference would suggest that the Israelites were familiar with the Nephilim.

Numbers 13:30-33
30 Then Caleb silenced the people before Moses and said, "We should go up and take possession of the land, for we can certainly do it." 31 But the men who had gone up with him said, "We can't attack those people; they are stronger than we are." 32 And they spread among the Israelites a bad report about the land they had explored. They said, "The land we explored devours those living in it. All the people we saw there are of great size. 33 We saw the Nephilim there (the descendants of Anak come from the Nephilim). We seemed like grasshoppers in our own eyes, and we looked the same to them." NIV