Multiple and perhaps even most modern translations of the New Testament, such as the ASV, RSV, NASB (77 and 95), NIV, ESV, NET, and CSB, in some way indicate that Mark 16:9-20 are not original to Mark's Gospel. They do this in different ways, whether by placing these verses within square brackets and adding a footnote explaining their doubtful character, placing them in all italics, or perhaps inserting a note directly between verses 8 and 9 that says they "may" not be original.
In this way they cast doubt on their trustworthiness, and as a consequence cast doubt on whether these verses are authentically God's Word. They do this further by stating that "some" early manuscripts do not contain them, or that there are no early witnesses to them, or they baldly say they were "added" or "inserted" at some later date. Thankfully, we can know that they are incorrect.
We can know because St. Irenaeus, providentially, referred to this section of Scripture directly and explicitly. A faithful Christian theologian and apologist, St. Irenaeus lived in the Second Century, was born and raised in Asia Minor, and became a bishop of Lyon, in Gaul. Thus he had deep experience in both the Eastern and Western geographical territories of the Roman empire, and so was in an extremely good position to be cognizant of what constituted the authentic ending of the text of Mark's Gospel. He wrote:
[T]owards the conclusion of his Gospel, Mark says: "So then, after the Lord Jesus had spoken to them, He was received up into heaven, and sitteth on the right hand of God;" (Against Heresies, Book 3, Chapter 10, para. 5; Ante-Nicene Fathers, Vol. 1, eds. Roberts and Donaldson, Revised by Coxe, (Christian Literature Publishing Company, 1885), pg 426 )
That is a direct quotation of Mark 16:19, which in the Authorized Version is translated:
So then after the Lord had spoken unto them, he was received up into heaven, and sat on the right hand of God. (Mark 16:19)
Notice that St. Irenaeus does not simply quote this verse, but specifically describes its source as being from the conclusion of Mark's Gospel. For those who are interested in the Latin (the original Greek of St. Irenaeus' text is lost), it reads:
In fine autem Evangelii ait Marcus: "Et quidem Dominus Jesus, postquam locutus est eis, receptus est in cælos , et sedet ad dexteram Dei;" (Patrologia Graeca, vol. 7, Irenaeus, paragraph 188)
Interestingly, the foregoing Latin reads differently than the Vulgate (late 4th Century) rendering of that same Markan verse, indicating that this was not a later insertion into the text of Irenaeus:
et Dominus quidem postquam locutus est eis adsumptus est in caelum et sedit a dextris Dei (Mark 16:19)
The resulting conclusion is necessary: Providentially, we have a definitive early witness from the Second Century that explicitly identifies Mark's Gospel as ending ("in fine") well beyond verse 8. Not only this, the verse being quoted by St. Irenaeus indicates Jesus' prior speech to the Eleven Disciples, which is also providentially to affirm the intervening verses between 8 and 19. This shows that the place (not the "insertion") of those verses into Mark's Gospel are certain and necessary, and that to cast doubt on their presence is problematic, to say the least.
As a common logical fallacy is popularly summarized, absence of evidence is not evidence of absence, and so the fact that "some early manuscripts" may not contain those verses is not conclusive evidence that they were never there. And, as shown above, St. Irenaeus' witness to their positive presence at such an early date defeats the argument that they were a later insertion.
Moreover, the translation into English of St. Irenaeus given above is from the year 1885, post-dating the doubt cast upon those verses by the famous textual scholars, Westcott and Hort, in their 1881 Revised Text (which is the grandfather of the eclectic Greek texts from which most modern translations are taken). This not only vindicates the Majority and the Received Texts on this point, but also means that the affirmation of the integrity of the last twelve verses of Mark has been available for over a century. And yet still the (false) claim persists that there is not a definite, reliable witness to their presence.
Therefore, the modern translations which cast doubt on those verses would do well to remove any indication that they may not be original, or at the very least notate that they do indeed have some of the earliest and best Patristic witnesses to their genuineness (since the earliest extant copies of Mark's Gospel are well over a century after St. Irenaeus).