The Old Testament has 593,493 words, and the New Testament has 181,253 words. So that makes a total of 774,746. These figures are for the Authorised Version or the King James bible, translated and produced in England in the 17th century. Some sources give the total number as 783,137 - it depends if you include things like the chapter list in your total.
For the modern versions of the Bible it is harder to arrive at an exact number because, unlike the Authorised Version, the modern bible doesn't have a single authoritative text but has been rewritten and retranslated several times. However, the count should be similar.
There are also 3,566,480 letters in the King James Bible, and a total number of 66 books. It is still apparently the top selling book in the world although not one of the most read. If you are interested in facts like these you may like to have a look at this page.