Depending on your Bible translation, you will either have or lack Matthew 17:21; 18:11; 23:14; Mark 7:16; 9:44, 46; 11:26; 15:28; Luke 17:36; 23:17; John 5:3b-4; Acts 8:37; 15:34; 24:6b-8a; Rom. 16:24; 1 John 5:7b-8a. Older translations contain them, such as the King James and New King James. Newer versions, however, do not. Since the KJV and NKJV are among the oldest English translations, they are often pointed to as the standard of English translations. Yet, just because they are “older” English translations doesn’t mean they are the best.
The very first Greek New Testament to be comprised was by Erasmus in 1516. He used 12th-century manuscripts of the New Testament. Remember that we’re focusing on the New Testament, translated from Greek. There was a Greek Old Testament, the Septuagint, in Jesus’ day. Nevertheless, at Erasmus’ time, the oldest manuscript was from the 10th century, but he opted for those from the twelfth century. As time passed, scholars made revisions that echoed Erasmus’ text. Most English translations through 1880 used the same Greek New Testament, called Textus Receptus (“received text”).
By the 1700s, many more manuscripts had been discovered. Some were six to nine centuries older than what Erasmus had available. These older manuscripts lacked the passages mentioned earlier. A common belief was that a scribe may have mistaken an explanatory marginal comment for a correction and copied it into the text, which accounts for why older English translations have a few more verses. A new Greek New Testament was made and appeared in 1831. Since the manuscripts were older than Erasmus used, they omitted the sixteen passages to construct a more ancient version, reflected in many English translations today.
Since 1611, the King James Bible has reigned as the preeminent English translation. However, because of the newer Greek New Testament, a Revised Version was commissioned in England in 1881. The Revised Version would later birth the New Revised Standard Version, which would later birth the English Standard Version. When the Revised Version appeared, there was a considerable uproar since the long-dominant KJV had set the standard. The omission of the verses was seen as blasphemous, and people cited Revelation 22:19 to those who upheld the Revised Version. Revelation 22:18 is more relevant if you want to argue the point.
Translations that omit these added verses usually contain a footnote or marginal note explaining that they appear in later manuscripts. Modern translations do not leave these verses out per se any more than the older ones added them. They are simply the product of the information available at the time. Now that we have older information, the translations that omit them should be more commonly used.
More recent translations utilize a vast amount of sources. The standard for most English translations is the Masoretic text of the Hebrew called Biblia Hebraica Stuttgartensia; the Greek New Testament used is Novum Testamentum Graece. Translators often consult, alongside these sources, the Dead Sea Scrolls, the Septuagint (Greek Old Testament), the Samaritan Pentateuch (Law of Moses), the Syriac Peshitta (Syriac Bible), the Latin Vulgate, and other sources that may help shed light on texts that may be difficult to translate.