The Bible I have in my possession today is not innerrant because there have been slight copyist errors down through history and also errors in translation between languages. I think this has been proven.
However, I choose to believe that the Bible, in its original manuscripts was totally without error. I base this on a variety of reasons.
#1 "All scripture is given by inspiration of God and is profitable for doctrine, for reproof, for correction, for instruction in righteousness" - 2 Tim. 3:16
If God cannot "inspire" something that is totally correct then He would have to be a liar. One Bible passage states God cannot lie. The Bible also condemns prophets as totally false who are proven to teach anything false even if the other 99% of what they prophesy proves correct.
#2 It has been proven that there has been a high degree of reliability in the the transmission through history of scripture by the discovery and comparsion of ancient manuscripts. I have also heard that we have far fewer copies of other ancient documents and still we regard their transmission/copying as basically accurate.
#3 God proves He is concerned about accuracy of the scriptures by warning judgment on those who knowingly alter it (ie. Revelation 22:19). See also Matt. 5:18.
#4 The Bible is self-proving to someone who wants to seriously search it out because of the combination of words and teachings written over hundreds of years (by people who did not directly know each other) which all echo a common theme. The fact that there are a majority of Jews who deny Christ yet still hold to the Old Testament proves that there could not be collusion between Christians and Jews through out history in compiling the present Bible. I believe the Old Testament time and time again proves Jesus Christ and the only explanation for that has to be supernatural.
#5 Some religions cite certain individual people as their source of revelation (ie. Muslims point to Mohammed, who is now dead). I can point to an entire nation of witnesses (Israel) who are not only still alive but organized into a nation state! (Fullfilling yet another ancient prophecy in Ezekiel.) Israel is a race of people whose physical existence has a basis in a rather unusual call by God to not only Abraham (which Muslims also believe) but also Isaac and Jacob. Even secular Jews should refer at least in part to the books of Moses to explain their history. You may say, well by that standard of argument isn't every Muslim a witness to the accuracy of Mohammed? Maybe. However, I'm not even beginning to address the testimony of millions of Christians around the world but only that of unbelieving Jews!
#6 Parts of the Bible that were thought to be inaccurate or odd in the past have been found to be portals to deeper meanings which proves the Bible's supernatural origin (ie. see Chuck Missler's book Hidden Treasures in the Biblical Text).
#7 The Bible teaches that faith is required to please God, therefore it is possible to assume by faith that the people who complied the books of the Bible were under the influence of God's Holy Spirit. In other words, I can believe even if I don't see all the absolute evidence.
I could go on and on explaining the inadequecy of the the theory of evolution in explaining all life, scientific evidences in the Bible, etc...
I choose to believe that the Bible is a supernatural book telling of a supernatural Jesus Christ who is God existing from before time began. Since He is God, His blood sacrifice is sufficient to atone for, as one preacher puts it, "the sum total of all human existence". I buy into this atonement by also believing in His supernatural resurrection. Finally, since the orgin of the Biblical message is so supernatural there is also limited sense in trying to explain it all in human terms.