The chapter and verse divisions found in virtually all modern Bibles originated on the mid 16th century:
Robert Estienne created an alternate numbering in his 1551 edition of the Greek New Testament which was also used in his 1553 publication of the Bible in French. Estienne's system of division was widely adopted, and it is this system which is found in almost all modern Bibles.
However, the best Greek NT available at the time was Erasmus’ Received Text. Since that time significant older and more reliable manuscripts have been discovered. In the late 19th century two Christian scholars, Wescott and Hort, compiled a “critical Greek text” for the NT. They utilized (and in some cases pioneered) scientific methods of textual criticism to propose the most likely original text of the NT. The New World Translation (a Jehovah Witness translation of the Bible which is considered by most Christians to be heretical) is based on WH’s Greek NT to this day. WH proposed that these verses are not original to John so the Jehovah Witness translators leave the passage out entirely.
Most modern translations (the NKJV being a notable exception) are based on the Nestle-Aland Greek NT and the United Bible Society’s Greek NT (now identical texts). These critical NT compilations follow in the tradition of WH but take into account even more recent manuscript discoveries. Furthermore the NA and UBS Greek NTs list many variations of the text in footnotes and note which significant manuscripts contain what.
Most modern Bible translations retain this passage for historical and traditional reasons but place it within brackets to denote that the verses may not be original to the Gospel of John. The ESV Study Bible states:
There is considerable doubt that this story is part of John’s original Gospel, for it is absent from all of the oldest manuscripts. But there is nothing in it unworthy of sound doctrine. It seems best to view the story as something that probably happened during Jesus’ ministry but that was not originally part of what John wrote in his Gospel. Therefore it should not be considered as part of Scripture and should not be used as the basis for building any point of doctrine unless confirmed in Scripture.
(ESV Study Bible on John 7:53-8:11)