The New King James Bible is the standard (most commonly used) bible for English speaking people (Americans), but it has gone through multiple translations mostly to suit new beliefs and (or) use of language. Christians today can't wholly agree on which bible is doctrine as there are several translations in use. It can be difficult to translate word for word from one modern language to another due to changes in grammar and meaning, and shifts in nuance for individual words. I assume it can be even more difficult to translate foreign languages of the past due to the same problems compounded by the loss of first hand speakers for clarity. How accurate are modern bibles like the New King James Version to the original aramaic? What is known to be lost in translation that is often misinterpreted today? Are there any passages that are thought or known to be deleted from or added to today's translations?
Edit: altered two phrases to appease disgruntled commentors.
Also, to settle the translation, interpretation debate. Translation: definition 1.1 according to the Oxford Dictionary. "A written or spoken rendering of the meaning of a word or text in another language."
Translation assumes interpretation. They are synonymous in this question. "Ich bin ein Berliner" translates to both "I am a citizen of Berlin" and "I am a Jelly Donut". Accurate translation requires accurate interpretation.
I've seen studies and surveys that claim anywhere from 31-55% of Christians read the New King James Version. In all cases the NKJV is the most commonly read, therefore my inaccurate "standard" claim. I can find no studies done that have a global investigation of English speakers. Bible scholars prefer the New Revised Standard Version. Perhaps someone will include that disconnect in their answer.
How accurate are modern bibles like the New King James Version to the original aramaic?
One nitpick--a relatively small portion of the bible is in Aramaic. The Hebrew bible is almost all Hebrew, and the New Testament is entirely Greek (with a few Aramaic words and phrases thrown in).
This question is not quite answerable as-is, for a couple different reasons:
Are there any passages that are thought or known to be deleted from or added to today's translations?
There are different textual sources one could use to write a bible translation. It's possible to pick one and declare everything not in your preferred manuscript source as "missing", but that's not really accurate. For instance, the Ancient Greek versions of the bible have significant additions to the Book of Esther. Jewish translations never include this, and Christian ones only sometimes do, often relegating it to an appendix in the back. Is it "missing" from those? No, they just decided to use a source text that omits it. This isn't a crazy decision, since it's likely that the additions to Esther were written later than the basic text as it exists in both Greek and Hebrew versions.
There are Christian bible translations that translate the Septuagint (an ancient Greek version of the bible) instead of the Masoretic Text (the conventional Hebrew text). It's not necessarily wrong to pick one over the other, it's simply a choice of what the "authoritative" bible text is you're working with. Very often bible translators will mainly translate one source text, but footnote possible alternate readings from other bible source material.
This problem isn't unique to bible translation, either. Shakespeare's King Lear exists in several versions with significant differences. The "conventional" text you'd find in a regular edition is a mish-mosh of two versions. Was the editor wrong to not include both? Are lines present in one of the source texts but absent in the other, and absent from the "normal" modern edition, "missing"? Or, if they were included, are they "extraneous additions"? Further, King Lear was historically often performed as a comedy, with a completely different ending than Shakespeare wrote it. And there are King-Lear-based plays, like *Der Yiddisher Kenig Lear" which are supposed to be translations, but are actually substantial reworkings. If I wanted to publish a play "King Lear, as Jewish immigrants in the 1920s would've experienced it", would I be wrong to use the 1892 Yiddish version, rather than either one of Shakespeare's originals?
To bring this back to the bible, nJPS (a common Jewish translation) almost exclusively uses the Masoretic Text (the "standard" Hebrew text), occasionally footnoting when a variant reading or Dead Sea Scroll manuscript or a Septuagint reading makes more sense. They didn't delete all parts of the bible not included in the Masoretic text, they just wanted to translate the standard Hebrew text. Theology definitely influenced their decision, but it's not necessarily a wrong one.
It's not like modern translations are simply editing things out or adding things in. They're picking between biblical manuscripts which have more or less material.
How accurate are modern bibles like the New King James Version to the original aramaic? What is known to be lost in translation that is often misinterpreted today?
In terms of actual wording, the vast majority of difference between bible versions will simply be word choice. Words often don't have neat 1:1 mapping across languages. There are also words that have unclear meaning. The normal Biblical Hebrew conjunctive, which technically is "and", often seems to be a broadly used conjunctive, where we might use "so" or "then" or nothing at all. How slavishly we translate it as "and" or fill in a conjunctive that works better is a translator's choice, but really a right or wrong decision. Translating it as "and" might be more technically close, but produces an English text which is weird and repetitive in a way the Hebrew isn't. Then there are words with unclear or obscure meaning, which is again often a translator's choice.
But what I think you're getting at is theologically motivated word choice. This definitely happens. There's the "virgin" of Isaiah 7:14, where Christian translators pick the wording of the Greek text instead of the Hebrew for theologically motivated reasons (namely, that in the Christian bible that's the reading they seem to use). Some translations do this more than others, and /r/academicbiblical has already given you some specific recs. But very often the theologically motivated word choice is simply picking one of several possible translations that makes the most sense for theological reasons, not making things up whole-cloth.
And needless to say there's no way to assess what reading of a particular passage is "the most accurate". For most translation choices there's simply no way to know.
Just to let you know, you might try cross-posting this to /r/AcademicBiblical to get the perspective of Bible scholars.