I'll weigh in. I am a Christian, and I believe in the literalness of the Bible, yet I also believe that there were dinosaurs, neanderthals etc and the earth is hundreds of millions or more years old, and I see no contradiction between these two apparently opposing conclusions.
Christians base the "6,000 year old earth" thesis on a reconstruction of a loose timeline based on ages and dates of characters given in the Bible. If Noah lived this many years, and this person lived this many years, and Jesus was born around AD 1, then we know...
It is on these grounds, and on the conviction that the Bible is the word of a God that never lies and is never wrong, that the age of the Earth is determined to be only 6,000 years, and no amount of "science" could change such a Christian's mind.
It is my contention, though, that it is not God or the Bible who is mistaken, nor is it science, but rather it is often man in his mistranslation of the Bible, and this is a case in point:
Genesis 1:1 is very familiar, and says "In the beginning God created the heavens and the earth." Genesis 1:2, slightly less familiar, says in many English translations, "And the earth was void..." However, when one looks to the original Hebrew, the verse is actually "And the earth became void..." Also, Isaiah 45:18 says, from the original Hebrew, that God did not create the earth waste, or void. This is significant because it indicates that God, who is perfect created a perfect earth (how could imperfection come out of perfection? wouldn't that prove that God himself is imperfect?), but something happened. This something, according to the Bible, was the fall of Lucifer/Satan, which preceded a rebellion, or a war of sorts. This may have been quite devastating to the earth at that time. Anyway, the point is, the Bible itself indicates that an indefinite amount of time passed between God's creating a perfect heaven and earth and earth's subsequently becoming void. Any number of cataclysmic events, changes in geology, flora, fauna et cetera could have happened; these changes, however, are basically irrelevant to the narrative of the Bible, and so are left out. It was only after this series of events that God came in to recreate the world "in 7 days".
Of course, for the many atheists who will read this, this is simply more fairy tales and they will be unconvinced; my message to them is that whether you believe the Bible or not, it is important to at least give it a fair hearing, to see that it is often misrepresented, not only by non-believers, but even more often by believers themselves. As to any Christians who may read this, you should consider the possibility that the Bible and science are actually in harmony, and it is simply a failure on man's part to understand what the Bible is saying.
I apologize for such a long post, but I felt it was necessary to spend a little time elaborating my point of view.