Arguably, no single book has been translated into more languages than the Bible. Originally written in Hebrew, Aramaic, and Greek, at least part of the Bible has been translated into thousands of languages around the world.
Arguably as well, no single book has influenced the world more than the Bible -- for both good and ill. Whether one is a believer or not (and frequently, non-believers know more about the Bible than believers!), basic knowledge of the Bible is necessary to understand the backgrounds of Western Civilization (to say nothing of all those allusions in Shakespeare!)
This list is presented chronologically, and does not include partial translations or paraphrases.