There are two basic versions of the fallen angels story: the fall of theWatchers, discussed here, and the fall of Lucifer. The Watchers were the “sons of God” who took human wives, and had children. Their children were known as the Nephilim.

Watchers in the Old Testament

“When men began to increase on earth and daughters were born to them, the divine beings saw how beautiful the daughters of men were and took wives from among those that pleased them. The LORD said, ‘My breath shall not abide in man forever, since he too is flesh; let the days allowed him be one hundred and twenty years.’ It was then, and later too, that the Nephilim appeared on earth – when the divine beings cohabited with the daughters of men, who bore them offspring. They were the heroes of old, the men of renown.” – Genesis 6:1-4
This is the only account of the watchers in the Bible. Isaiah 14:12-15 talks of the fall of the “day-star, son of morning,” which implies that there was a revolt, and the “day-star” was cast into the abyss, but this may be a reference to early Canaanite or Phoenician myths. One other possible reference is Psalm 82.
God standeth in the Congregation of God (El)
In the midst of gods (elohim) He judgeth
All the foundations of the earth are moved.
I said: Ye are gods,
And all of you sons of the Most High (Elyon)
Nevertheles ye shall die like men,
And fall like one of the princes (sarim)
Psalm 82:1, 5-7
The parts of the Psalm I have left out are the parts that refer to wicked earthly rulers, but it is agreed upon by many scholars that this part of the Psalm refers to the fallen angels. While Genesis 6 tells that angels married women, it does not condemn this as a sin. Psalm 82 tells that the elohim sinned, but does not tell how (i.e. it does not mention that they married women).

Some rabbis have speculated that the angels’ sin was to reproduce. Certainpassages in Jewish Midrash talk of how angels are immortal and do not need to reproduce. Since humans are not, they must reproduce in order to achieve immortality in their descendents.

Watchers in Jewish Midrash

This is a passage from Jewish midrash in which Hannah is praying for a child at Shiloh:
“Lord of the Universe! The celestials never die, and they do not reproduce their kind. Terrestrial beings die, but they are fruitful and multiply. Therefore I pray: Either make me immortal, or give me a son!” 

Watchers in 1 Enoch (Part 1)

A different interpretation of this passage concerning the sin of the angels was that they revolted against God, and because of this, they were cast down. Apocrypal texts give more complete accounts of the fall of the angels. (For more about texts found outside the bible, see Pseudepigrapha and Enoch)

1 Enoch gives an account of the fall of the Angels from heaven. Chapter 6 talks of how the angels saw and lusted after the daughters of men.
“In those days, when the children of man had multiplied, it happened that there were born unto them handsome and beautiful daughters. And the angels, the children of heaven , saw them and desired them; and they said to one another, ‘Come, let us choose wives for ourselves from among the daughters of man and beget us children.’ And Semyaz, being their leader, said unto them,’I fear that perhaps you will not consent that this deed should be done, and I alone will become (responsible) for this great sin.’ But they all responded to him, ‘Let us all swear an oath and bind everyone among us by a curse not to abandon this suggestion but to do the deed.’ Then they all swore together and bound one another by (the curse) And they were altogether two hundred;” – 1 Enoch 6:1-7 
The angels descended on Mount Hermon during the days of Jared. There were 19 leaders mentioned in 1 Enoch, who were also called ‘the chiefs of ten.’ Once they reached the earth:
“they took wives unto themselves, and everyone (respectively) chose one woman for himself, and they began to go unto them. And they taught them magical medicine, incantations, the cutting of roots, and taught them (about) plants. And the women became pregnant and gave birth to great giants whose heights were three hundred cubits. These (giants) consumed the produce of all the people until the people detested feeding them. So the giants turned against (the people) in order to eat them.” – 1 Enoch 7:1-5 
The Angels then taught women charms, enchantments, the cutting of roots, and the knowledge of plants. They taught men how to make various weapons and armor, and also arts and sciences. These acts led to an increase in lawlessness and warfare. The men of earth then cried out to heaven, and the 4 archangels (Michael, Uriel, Raphael, and Gabriel) cried out to God. In response, God sent Uriel to warn Noah that there would soon be a flood that would destroy the wickedness on earth.

Raphael was commanded to bind Azazel hand and foot, and to cast him into the a hole in the desert (Duda’el) that the Lord had made. Raphael threw rugged and sharp rocks and covered Azazel’s face so that he would not see light. Michael was commanded to bound Semyaza and his associates in the valleys of the earth. They will remain there until the day of judgment when he will be cast into the fire.

The race of giants produced from this union gave way to a brood of evil spirits. The evil spirits most likely are the departed spirits of the giants, themselves. These spirits are not material or corporeal beings, but they torment mankind because they have proceeded from them. According to 1 Enoch, these spirits will not be punished until the day of judgment, in contrast to the Watchers, who are punished both before and on the day of judgment.
“But now the giants who are born from the (union of) the spirits and the flesh shall be called evil spirits upon the earth, because their dwelling shall be upon the earth and inside the earth. Evil spirits have come out of their bodies. Because from the day that they were created from the holy ones they became the Watchers; their first origin is the spiritual foundation. They will become evil upon the earth and shall be called evil spirits. The dwelling of the spiritual beings of heaven is heaven; but the dwelling of the spirits of the earth, which are born upon the earth, is in the earth. The spirits of the giants oppress each other, they will corrupt, fall, be excited, and fall upon the earth, and cause sorrow. They eat no food, nor become thirsty, nor find obstacles. And these spirits shall rise up against the children of the people and against the women, because they have proceeded forth (from them). – 1 Enoch 15
1 Enoch 19 also gives a variation to the origin of demons. It implies that demons were already in existence during the time of the fall of the angels. According to 1 Enoch 10-16, the demons are the spirits which go forth from these angels.
“Here shall stand in many different appearances the spirits of the angels which have united themselves with women. They have defiled the people and will lead them into error so that they will offer sacrifices to the demons as unto gods, until the great day of judgment in which they shall be judged till they are finished.” – 1 Enoch 19:1 
1 Enoch 85-90 gives a similar account of the fall of the angels. In these passages, a star (either Semjaza or Azazel) fell from heaven and began to pasture among the oxen (mankind). A number of stars then fell and were transformed into bulls. They began to cover the cows (the angels married mortal women), who then gave birth to elephants, camels, and asses (the giants). The oxen then became restless and began to fight, but they became prey to the wild beasts. The archangels then appear in the disguise of men. One seizes the first of the fallen stars and casts it into the abyss. A second gives the elephants, camels, and asses a sword so that they will slay each other. A third archangel stones the other fallen stars and casts them into the gulf. The story then goes on to describe the Maccabean revolt, which leads to a description of the final struggle between good and evil.

It seems that there is a threefold aspect to the sin of the Watchers in these accounts. First, it was a defilement of the essence of the angels to marry and engage in sexual acts with human women. Second, these unions between the angels and mortal women were considered evil, themselves. Because of the Nephilim and and evil created by these unions, God caused the great Flood of Noah’s time. Finally, the angels sinned because they taught humanity and revealing the secrets of the natural universe which God did not intend for man to know.

Watchers in The Book of Jubilees

The Book of Jubilees gives another account of how the Watchers fell that is similar to 1 Enoch. It explains that the Watchers originally descended to the earth to teach mankind and do what is just, but they ‘sinned with the daughters of men because these had begun to mix with earthly women so that they became defiled.’ (Jubilees 4:22)

Malalael “named [his son] Jared because during his lifetime the angels of the Lord who were called Watchers descended to earth to teach mankind and to do what is just and upright upon the earth” –Jubilees 4:15

Jubilees also says that they were sent by God, Himself.
“Against his angels whom he had sent to the earth he was angry enough to uproot them from all their (positions of) authority” –Jubilees 5:6 
Jubilees tells an account of the fall of the angels similar to that of 1 Enoch. God was displeased with the angels because of their lust for the daughters of men. The union of the angels and women is said to be the Nephilim.
“For it was on account of these three things [fornication, uncleanness, and injustice – see Jubilees 7:20] that the flood was on the earth, since (it was) due to fornication that the Watchers had illicit intercourse – apart from the mandate of their authority – with women. When they married of them whomever they chose they committed the first (acts) of uncleanness. They fathered (as their) sons the Nephilim. – Jubilees 7:21-22
In Jubilees, Mastema is the chief of the spirits. As God commanded the angels to bind all the evil spirits, Mastema came and asked the Lord that some of the spirits might be allowed to remain with him to do his will. God granted his request and allowed one tenth of the spirits to remain with Mastema, while the other nine parts would be condemned.
“When Mastema, the leader of the spirits, came, he said: ‘Lord creator, leave some of them before me; let them listen to me and do everything that I tell them, because if none of them is left for me I shall not be able to exercise the authority of my will aong mankind. For they are meant for (the purposes of) destroying and misleading before my punishment because the evil of mankind is great.’ Then he said that a tenth of them should be left before him, while he would make nine parts descend to the place of judgment.” –Jubilees 10:8-9

Watchers in 2 Enoch

2 Enoch also mentions a group of angels called the Grigori, who are similar to the Watchers. Their prince is called Satanail. A difference in this account as compared with the two previous accounts is that only 3 angels came down to earth to take wives and beget giants.
“These are the Grigori, who with their prince Satanail rejected the Lord of light, and after them are those who are held in great darkness on the second heaven, and three of them went down on earth to the place Ermon, and broke through their vows on the shoulder of the hill Ermon and saw the daughters of men how good they are, and took to themselves wives, and befouled the earth with their deeds, who in all times of their age made lawlessness and mixing, and giants are born and marvellous big men and great enmity. And therefore God judged them with great judgment, and they weep for their brethren and they will be punished on the Lord’s great day.” – 2 Enoch 18:3-4

Watchers in Testaments of the Twelve Patriarchs

In the Testaments of the Twelve Patriarchs, the fall of the angels is mentioned twice. One is only a brief reference stating that the Watchers “changed the order of their nature.” (Naphtali 3:5) The second is in Reuben, where he accuses womankind of seeking to ensnare men.
“Thus they allured the Watchers before the Flood, for as these continually beheld them, they lusted after them and conceived the act in their mind; for they changed themselves unto the shape of men and appeared to them when they were with their husbands; and the women, lusting in their minds after their forms, gave birth to giants, for the Watchers appeared to them as reaching up to heaven.” (Reuben 5)
In this account, the writer denies that there was a physical union between the angels and mortal women. He says that the real fathers of the giants were humans, but the giants were conceived from the mutal passion from angels and women.

Flavius Josephus’ Antiquities of the Jews

Flavius Josephus,a Palestinian, wrote his Antiquities of the Jews to educate the Roman-Hellenistic world about Judaism and the Jews. In it, he recounts the tale of the Watchers as follows:
For many angels of God accompanied with women, and begat sons that proved unjust, and despisers of all that was good, on account of the confidence they had in their own strength; for the tradition is, that these men did what resembled the acts of those whom the Grecians call giants. But Noah was very uneasy at what they did; and being displeased at their conduct, persuaded them to change their dispositions and their acts for the better: but seeing they did not yield to him, but were slaves to their wicked pleasures, he was afraid they would kill him, together with his wife and children, and those they had married; so he departed out of that land. – 1.72-75 
According to Josephus, the union between the fallen angels and human women produced a race of giants, which in antiquity were called Nephilim.

Philo’s Commentary on Genesis 6

Philo of Alexandria (20 B.C.E.-50 C.E.) wrote a commentary of Genesis 6 called Concerning the Giants. In it, he emphasized that the passage was not a myth.
“And when the angels of God saw the daughters of men that they were beautiful, they took unto themselves wives of all of them whom they Chose.”{#ge 6:2.} Those beings, whom other philosophers call demons, Moses usually calls angels; and they are souls hovering in the air. And let no one suppose, that what is here stated is a fable, for it is necessarily true that the universe must be filled with living things in all its parts, since every one of its primary and elementary portions contains its appropriate animals and such as are consistent with its nature; –the earth containing terrestrial animals, the sea and the rivers containing aquatic animals, and the fire such as are born in the fire (but it is said, that such as these last are found chiefly in Macedonia), and the heaven containing the stars: for these also are entire souls pervading the universe, being unadulterated and divine, inasmuch as they move in a circle, which is the kind of motion most akin to the mind, for every one of them is the parent mind. It is therefore necessary that the air also should be full of living beings. And these beings are invisible to us, inasmuch as the air itself is not visible to mortal sight. (But it does not follow, because our sight is incapable of perceiving the forms of souls, that for that reason there are no souls in the air; but it follows of necessity that they must be comprehended by the mind, in order that like may be contemplated by like.
– Philo, On the Giants II: 6-9

Names and Misdeeds of the Watchers

Names and Misdeeds of the Fallen Angels (aka the Five Satans) in 1 Enoch 69:4-12. (1 Enoch gives other lists of the names of the fallen angels as well.) This passage is odd because it mentions angels that are not mentioned elsewhere.

1. Yeqon – “one who misled all the children of the angels, brought them down upon the earth, and perverted them by the daughters of the people”
2. Asb’el – “one who gave the children of the holy angels an evil counsel and misled them so that they would defile their bodies by the daughters of the people”
3. Gader’el – “he who showed the children of the people all the blows of death, who misled Eve, who showed the children of the people (how to make) the instruments of death (such as) the shield, the breastplate, and the sword for warfare, and all (the other) instruments of death to the children of the people”
4. Pinem’e – “demonstrated to the children of the people the bitter and the sweet and revealed to them all the secrets of their wisdom. Furthermore he caused the people to penetrate (the secret of) writing and (the use of) ink and paper”
5. Kasadya – “he who revealed to the children of the people (the various) flagellations of all evil – (the flagellation) of the souls and the demons, the smashing of the embryo in the womb so that it may be crushed, the flagellation of the soul, snake bites, sunstrokes, the son of the serpent, whose name is Taba’ta”

Names of other fallen angels – Semyaz, Aristaqis, Armen, Kokba’el, Tur’el, Rumyal, Danyul, Neqa’el, Baraqel, Azaz’el, Armaros, Betryal, Basas’el, Hanan’el, Tur’el, Sipwese’el, Yeter’el, Tuma’el, Tur’el, Rum’el, and Azaz’el – 1 Enoch 69:2