There are two different compilations of the Greek text used by Bible translators. To simplify it, these are:
- The Textus Receptus / Received Text / Byzantine Majority Text. This is the text that has traditionally been used by most of the Church for most of the last two millenia up until about 150 years ago - hence it is the "majority" text. It generally includes more words.
Key English translations using this text: KJV, Geneva, WEB. You can also expect other old Bibles like the Latin Vulgate and Kevin's 6th century Aramaic version to align more with this.
- The Westcott-Hort / Nestle-Aland / United Bible Societies text. This is a selection of the oldest documents that is generally accepted by the majority of scholars to represent the original text (whether that's correct is debatable but beside the point). This text is shorter and omits many words and even entire passages that appear in the Textus Receptus / Majority Text.
The United Bible Societies publishes a Greek text for translators based on this textual variant (including the majority text as alternative notes), and most translators work from that by default. As a result, almost all modern translations come from this text.
Key translations: NIV, NKJV, and almost every other translation from the last 100 years.
Almost every single difference between the KJV and any other translation come down to this choice of different Greek text. Almost every argument a KJV-only believer makes as to why the KJV is better comes down to this difference in text.
And this issue of "wife" comes back to it also. It isn't that the bible translators of a whole lot of versions have independently decided to delete a word. It's that the men who compiled the Greek text they are using decided to choose a text that omitted that word, and all the translators are working from that text.
Which is right? Well on this matter it really doesn't make any theological difference so it doesn't really matter. I'm just pointing out that it's not an anti-polygamy conspiracy, just a symptom of something else.