Wow, this is a fun one. Without going into the technical level a number of other posters have (incredibly interesting, by the way), let's see if we can agree on a few basic timeline details.
The Torah (making up the majority of the Old Testament in the cannonical Bible in all modern Christian forms) is the Holy Book and writings of the Jewish peoples and their faith, containing within it the history and teachings that guide them to this day. It was originally written (and continues to be in Jewish faiths, synagogues, and houses) in Hebrew, and was later translated into Greek, as that was the official "language of learning" common to the Ancient World. This brought us to the time of Jesus.
Jesus was a teacher and leader of Jewish religious followers. He spent his time teaching according to the traditions and knowledge of his time, with his emphasis being different to the orthodoxy of the Pharisees etc. However, he was known and refered to as "rabbi", meaning "teacher'. The term does not specifically mean religious (the same way that "sensei" does not necessarily refer to a martial art teacher), however at the time religious teachings guided all other teachings, so you can read into that quite easily.
So my big issue here is when people are talking about "Christians of Jesus' time". There weren't any. They were Jews who followed Jesus, as there were Jews who followed many other Messianic Prophets at the time. Christians came later.
In terms of contemporary writings (I think maunakumu was saying that there are none for us to check...), there are quite a variety of writings from the time of Jesus, most famously the Dead Sea Scrolls, as well as a number of books that have been preserved in texts such as the Ethiopian Bible, and the Koran, and a number of other known "apocryphal" texts. So we can check them if we want to.
The translation issue, of Hebrew to Greek, to Latin, to English, or straight to English without going to Latin to begin with, well, the issues with translating from the original Hebrew has been covered very well. But I would add one more point, I beileve it was Brother John who said that his copy has three lines in various transliterations? Well, that's all well and good, but the job of a translation is far more than just "this word equals this other word". Context must be taken into account, as must personal idioms, particular (unique) phrases, cultural beliefs and practices which may or may not still be known or practiced, and more. And this is doubly important when dealing with a document such as this.
If there are there lines, with the first being the original Hebrew/Greek in the original lettering, and the second being the phonetic sounding of the text, that's all good. If you can understand it and read it. The third line is where we get a bit of trouble. If it is a direct word-for-word translation, then you are probably missing a great deal of information (as indicated above). A better (and more reliable) translation method is to translate in the context of the original, with it's spirit and heart. Every foreword I have ever read by a translator stresses that fact whether it is Homer, or Hatsumi.
By the time Constantine turned the Roman Empire Christian (and employed the Council of Nicea to address the issue of an official cannonical Bible), there had been a variety of texts moving throughout Christian circles for a few Centuries. Some of these stayed, others were taken out of the equation, and others survived in other sources (as earlier stated). Those that were kept were kept for a variety of reasons, including established authenticity, and congruence, as well as supporting a certain agenda of the new regime (for example, the anti-Roman sentiment which was a big selling point in the time of Jesus and directly following such was downplayed, and the new scapegoats used were the Jewish peoples themselves... I always found that rather ironic, the Jewish people gave the Romans their new religion [in a manner of speaking], although it was the Roman's who were directly responsible for the excecution of Jesus, and in return, the Jewish people get blamed and distanced from the new religious movement, in order to bring it more palatability to the Roman people. Go figure). Those that were removed were taken out for much the same reasons, although there were a few taken out because of simple story-telling rules (a lot of the stories about Mary, Jesus' mother are removed, including the fact that she is in fact the Immaculate Conception, rather than Jesus), as it takes the focus of Jesus. They have survived in the Koran, though, where Mary is mentioned far more than in the Christian Bible. Others were denied placement due to not going with desired ethics and values (in an extended version of the story of Genesis, for example, the question of Cain's wife is answered... the original [and I'm paraphrasing here] has Cain and Abel being the sons of Adam and Eve, and after Cain slays Abel, he goes off into the wild. Later he "knows" his wife, and she bears him a son. At this point, most astute and aware readers say "Hang on, Cain and Abel are the only children of Adam and Eve, where did the wife come from?". Well, this longer version has Cain and Abel simply being the two eldest of many children... and Cain's wife was therefore his sister. Although many other sins are demonstrated and allowed throughout the Bible in various forms, incest is a definate no-no. So the book couldn't be included).
Now, if we are to look at the Bible as being written by God Himself, then we may have an issue. Which books did He write? The ones we kept, or the ones we put aside? And did He write them Himself, or through people? Personally, I am not religious, but I believe that for a religious writer, the feeling is that God is writing through them, not that God is writing (the only case I can think of off the top of my head for God actually physically writing is on Mount Sinai when He incribed two stone tablets with the Ten Commandments for Moses to carry down to the People of Israel).
For those of faith, I have nothing but respect for you. If you believe the Bible is the literal Word Of God, that is your right and prerogative. However, if you are seriously researching the histories of these writings, you have no alternative but to acknowledge the role of human beings in the composition of the texts. And really, people, The Old Testament (the Torah) is the history and teachings of the Jewish People. End of story. It is a proud history of a proud people, the fact that it is downplayed in Christianity in lieu of the New Testament in no way diminishes or denies this very simple fact. It is theirs. We can study it, interpret it for lessons we can take with us, but unless you are Jewish, it is not your history. Okay?