The Old Testament was written in Hebrew.
The Apocrypha of the Old Testament was mostly written in Greek.
(There are a few disputed sections of some books (such as Daniel) that some scholars believe were originally written in Aramaic or Greek and translated to Hebrew, but those are not large passages and the conjectured original language is disputed).
The New Testament was written entirely in Greek.
(There is an ancient story that Matthew was originally written in Aramaic and later translated or re-written in Greek. Most scholars today do not support that story.)
The entire bible was translated into Latin (in what was then called the common, or vulgar, tongue and is now referred to as the vulgate).
The Authorized Version (aka the King James Version) was translated directly from the original Hebrew and Greek–except for a couple of sections for which King James’ scholars did not have good original sources, those were translated from the vulgate.
The Revised Standard Version is based upon the KJV, but since all the sources were available by the mid 1940’s, when it was written, it can be considered a translation directly from the original. Later translations such as the New International Version are all translated directly from the original languages.
The copies we have in original languages have a few possibly corrupted passages. However, the Jewish Masoretes attempted a complete correction of the text in the 9th and 10th (?) centuries. When copies of the Jewish testament were found at Qumran (the Dead Sea Scrolls), the Masoretes’ efforts turned out to have been amazingly good.
Similarly, the oldest complete texts of the New Testament date to the fourth century, but fragments dating to the second century have generally matched the later texts.
While it is possible that a few phrases has become lost or corrupted over time, the odds are pretty good that a modern translation is taken from a pretty accurate copy of the originals.