Previous Essays on the Ancestry of the King James Version are #1; #2; #3; #4; and #5 click on a link.
Opening Quotable Quotes
"A single hour lovingly devoted to the text of the Septuagint will further our exegetical knowledge of the Pauline Epistles more than a whole day spent over a commentary" (Adolf Deismann, 1908)
"We also remind the same class of readers, that an intimate acquaintance with the Septuagint Greek of the Old Testament, is of essential importance in translating the New. The seventy Hebrews ... gave to that translation the idiom of their vernacular tongue. Their translation, if I may so speak is a sort of Hebrew Greek. The BODY [sic] is Greek, but the SOUL [sic] is Hebrew ... we have no Greek by which to understand the apostolic writings, but the Greek of the Jewish and Christian Prophets" (Alexander Campbell, General Preface: An Apology for a New Translation of the Living Oracles in 1826).
The Need for an Ancient Translation
The need for a Greek version of the Hebrew Scriptures came from the historical reality the Jews found themselves in. After exile from their native homeland and then a pattern of migration to Egypt and other parts of the Hellenistic world hastened the loss the language of the ancestors. This migration had begun by Jeremiah's time. In Jeremiah 41-44 we learn of a band of Jews that fled to Egypt after the Babylonians destroyed Jerusalem in 587/6 BC (Jeremiah as you will recall was kidnapped and forced to flee with the bandits). Another group of Jews were garrisoned by the king of Egypt at Elephantine on the Nile. This Jewish colony even built a temple some time before 525 BC.
Beginning with the conquests of Alexander in 331, however, is when Jews settled in Egypt in large numbers. Alexander constructed the magnificent city of Alexandria to become one of the premier cultural icons of the Greek world. It would replace even Athens as the center of great learning and it had only one language - Greek. By the time Jesus was born over a million Jews lived in Egypt and many of those in Alexandria.
The Jews living in Alexandria, as in most Hellenistic environments soon lost the ability to speak or read Hebrew creating a crisis over hearing God's word. So sometime after 250 B.C. and down to around 150 B.C. the Septuagint (LXX) was born. Jewish legend (alluded to by Campbell above) preserved in the Letter of Aristeas explains the LXX's origins in the following way.
Aristeas was an official in Ptolemy Philadelphus' court, a renown patron of literature. Under Ptolemy the great library of Alexandria was built becoming one of the Seven Wonders of the Ancient World . Aristeas describes how Demetrius, the king's librarian, contacted Eleazar the High Priest in Jerusalem about obtaining translators to make a Greek translation of Jewish holy books for the library. So Eleazar chose six men from the twelve tribes. These men, after being honored, were sent to the island of Pharos where in seventy-two days the men finished their task. Later versions of the tale tell how the 72 men worked in separate cells and at the end of the 72 days they compared their work and found them to be exactly the same! The Letter of Aristeas is a tall tale of the origin of the Greek Bible but with more than a kernel of historical truth. But it is fascinating that everyone wants to claim divine inspiration for their particular translation.
As a historical tidbit. It seems that the first time the word "Bible" is ever used in reference to the Scriptures is in the Letter of Aristeas itself. In Aristeas verse 316 we read "I have also received from Theodectus the tragic poet (the report) that when he was about to include in a play a passage from what is written in the Bible, he was afflicted with a cataract of the eyes" (Old Testament Pseudepigrapha, vol 2, p. 34).
The Greek speaking Jews of Alexandria needed a Bible they could understand. Out of that need the Lord providentially worked and the LXX was born.
The Nature of the LXX
The LXX, as a translation of the ancient Hebrew text, is varied. In the Torah the translation appears to be very careful yet throughout the remainder of the "Old Testament" it is uneven. A wooden literalism characterizes sections of Reigns, Jeremiah, Song of Songs and Lamentations making for "awkward Greek." Conversely Esther, Job and Proverbs are much freer bordering paraphrase at times . The LXX reads at times, we have noted previously, quite differently than the Masoretic text (the text represented in most modern Protestant Old Testament translations). These differences can be attributed to several factors:
1) the underlying Hebrew text from which it was translated was different from the
2) the translation process was unprecedented and therefore does not reveal a pattern
3) the translator made a mistake
4) the theological understanding of the translator
5) a confluence of these circumstances produce varied results 
All of the books of the Hebrew Bible are contained within the LXX. However, one of the primary differences between the LXX and the "Old Testament" known to Protestants today is a collection of ancient writings often termed "The Apocrypha." (For more on The Apocrypha see HERE). The word "Apocrypha" means "hidden" which has lead to considerable misunderstanding for Protestants. This misnomer has almost taken on pejorative connotations with some but the term was not used in such a way by the ancients. Within the LXX these books are not distinguished from the rest of the Bible. Indeed most in the early church regarded them as if they were the word of God. These works are:
The Greek Esther has lengthy sections that are not present in the Hebrew Bible today
Wisdom of Solomon
Epistle of Jeremiah
Three lengthy sections of Daniel
2) Bel and the Dragon
3) The Song of the Three Children
Prayer of Manasseh
Some mss of the LXX also contain 3rd & 4th Maccabees. These books are also known as Deuterocanonical among Roman Catholics but simply Scripture among the Greek Orthodox, the Russian Orthodox, Ethiopian & Armenian churches. Contemporary scholarship debates the exact extent of the "Jewish" canon prior to 100 A.D. but it is certain that many Jews held these works in very high esteem if not as "scripture" itself prior to the Fall of Jerusalem. All English translations of the Bible used to include The Apocrypha between the "Old Testament" and the "New." These translations include: John Wycliff's, Coverdale's Bible, Matthew's Bible, Great Bible, Geneva Bible, Bishop's Bible, Rheims-Douay Bible, King James Version, the Revised Version, the Revised Standard Version, etc. Most "non-Evangelical" translations of Scripture have included the Apocrypha - RSV, NEB, REB, NRSV, JB, NJB, NAB, and even the ESV.
The NT writers themselves, contrary to oft repeated claims to the contrary, knew the stories and contents of these books. For example Paul alludes to the critique of pagan society in Wisdom of Solomon in Romans 1 and 2 several times. Psalm 151 preserved and known in the LXX for centuries was also discovered extant in Hebrew among the Dead Sea Scrolls. Here is the Greek version:
This psalm is a genuine one of David, composed when he fought in single combat with Goliath.
I was small among my brethren, and youngest in my father's
house, I tended my father's sheep. My hands formed a
musical instrument, and my fingers tuned a psaltery. And
who shall tell my Lord? the Lord himself, he himself hears.
He sent forth his angel, and took me from my father's sheep,
and he anointed me with the oil of his anointing. My brothers
were handsome and tall; but the Lord did not take pleasure
in them. I went forth to meet the Philistine; and he cursed me
by his idols. But I drew his own sword, and beheaded him, and
removed reproach from the children of Israel." 
The LXX and Early Christianity
The LXX, not the Hebrew Bible, was the primary theological and literary context within which the writers of the NT and most early Christians worked. It was THE Bible for the first three Christian centuries. In the 150 to 200 years it circulated prior to the advent of Christianity it enabled many Greeks to seek the God of Israel. The LXX's, in God's gracious wisdom, worked naturally as the perfect "missionary" tool of the early apostles, prophets and missionaries. The apostles did not have to invent theological terms for God's revelation in Christ, the LXX had already done that.
Words, important words, that continually grace the pages of the New Testament have a long history of use already in the LXX. Words for law (nomos), atonement (hilaskomai) ... words for truth, grace, mercy, sin, and even worship are all already in the vocabulary of Paul, Peter, John and most of all Jesus. These notions of mercy, grace, righteousness are hardly inconsequential for understanding "New Testament Christianity."
Yet the LXX's influence on early Christianity and the NT itself extends beyond simply word choices. The LXX was "biblical" language for many Jews in the same way the cadences of the King James Version is "biblical" language for many native English speakers. Luke often models his Greek after the biblical "sound" of the LXX. A Jew picking up the Gospel of Luke in the first century would "feel at home" in story. At times the LXX itself is actually the text of the NT. This happens through quotations of the "Old Testament" of which the vast majority in the NT come from the LXX. This fact, btw, often accounts for why a quotation from the "Old Testament" in may actually differ when one turns to the quoted passage . Beyond actual quotations the LXX provides the thought world and "allusions" that NT writers constantly weave into their writings.
A testament to the influence of the LXX in the early Christian centuries is found in the following numbers. More Greek mss of the "Old Testament" survive from antiquity than any other Greek text except the New Testament itself. Counting both complete and fragmentary mss, nearly 2000 handwritten copies of the LXX have come down to us.
As important at the LXX was in the early church it is mind blowing some King James Only advocates claim there was no such piece of literature before Christ. But Philo, the Alexandrian Jewish Philosopher, testified to his reverence for the LXX. For him Jews regarded ...
"them [Ancient Hebrew text & LXX] with awe and reverence as sisters, or rather as one and the same, both in matter and words, and speak of the authors not but as prophets and priests of the mysteries ... hand in hand with the purest of spirits, the spirit of Moses" 
Modern scholarship has basically confirmed the insight of Alexander Campbell and Adolf Deissmann quoted at the head of this post. The standard Greek lexicon proclaims in its Introduction "As for the influence of the LXX, every page of this lexicon shows that it outweighs all other influences in our literature" .
The NT writers "version of choice" was the LXX. The Greek speaking converts in the book of Acts, Paul's in Corinth, even the preacher "to the Hebrews" knew practically nothing of the Bible in its Hebrew original but only through this imperfect translation that proclaimed God's truth anyway - a valuable lesson here for us today!
The image above is a fragment of the LXX's Exodus.
 For a nice overview of the origin and significance of this wonder to its destruction at the hands of certain Muslims see Luciano Canfora, The Vanished Library: A Wonder of the Ancient World (University of California Press, 1987, 1990).
 See the fine, non-threatening, survey of these issues in Karen H. Jobes & Moises Silva, Invitation to the Septuagint (Baker Academic, 2000), 114ff.
 See Jobes & Silva's chapter "The Septuagint as a Translation," pp. 86-102.
 A translation from the Hebrew text can be found in The Old Testament Pseudepigrapha vol 2, p. 612f edited by James H. Charlesworth.
 This is sometimes not noticed by readers of versions like the NIV which will "conform" the Old Testament quotation to match the NT quotation.
 In C.K.Barrett, ed., The New Testament Background: Selected Documents, revised edition (SPCK, 1987), 294.
 A Greek-English Lexicon of the New Testament and Other Early Christian Literature, 3rd Edition (University of Chicago Press, 2000), xxii.