About 100 years ago (late 1800's and early 1900's) a common conclusion among Christian apologists was that Jews had edited the bible in order to remove Christological passages and in general to undermine Christian theology in the Old Testament. This claim was made due to advancements in Christian apology which admitted that many of the quotes made by New Testament authors (such as Paul or Matthew) had no foundation in the Jewish scriptures. The apologists concluded then that the Jews must have altered the old testament Hebrew so as to claim that the Christian texts were in error. Of course, this claim ignores the second possibility (that the Christians were the ones who altered the Hebrew). Luckily it is an easy matter to get to the bottom of this controversy once and for all.
The idea seems to make plausible sense at first glance; after all, would the writers of the New Testament really commit such a grave and grievous error? Would they really write something which was so obviously untrue? It would almost serve to undermine their case for Christianity. For if they were proven to be liars then obviously they would be false prophets. Therefore the claim is made that when the New Testament was originally written, the Old Testament would have read similar or exactly as written in the New Testament.
As this argument is made today it will usually hinge on the use of a translation such as the the Septuagint or the KJV. For example, Daniel 9:24-27 in the King James Version is well-known to be a remarkably poor translation; but (some) KJV-only enthusiasts (may) insist that it holds the original meaning and that (perhaps) sometime between now and 1611 the Hebrew scriptures had been altered. Even in cases where an alteration is not alleged, some people erroneously believe that the KJV is an inspired translation (see: Is the KJV inspired). Then (if the KJV was inspired, as the theory goes), the KJV could be granted ecumenical authority to alter doctrine as found in the Old Testament. This is only to admit that if and only if such a translation was authentic, preserved, or inspired, could it provide reasonable grounds for making the claim that the Hebrew scriptures had been altered instead.
It's unlikely for quite a number of reasons. First you will note that this was framed as a question often asked 100+ years ago. The reason why people stopped asking this question is because of the Dead Sea scrolls. All Christian scholars today admit that the Jewish scriptures we have today are virtually identical (99.9%+) to the text found in the Dead Sea scrolls – they have simply not been altered. Neither prior to, nor after the lifetimes of Herod, Jesus or Paul, or since then. Needless to say these texts all also concur with the Leningrad Codex and the Aleppo Codex. So we know in a very strong way now that the Jews have never added to or removed anything from the Bible.
In fact, most Christian apologists don't bother with this topic anymore because of the Dead Sea scrolls and the revival of Hebrew as a spoken language in Israel. To change this one would have to bring a significant amount of new evidence to the table. I don't think that is possible at this stage.
Further, it seems dangerous for the Christian to raise such an issue because it inevitably leads to a discussion on how the New Testament has corrupted the word of God, a statement which seems to have no easy response.
I've discussed this with numerous Christians and their first impression is generally, no, Jews did not do this. Further that it is an unrealistic assumption on multiple levels (the scriptures would have been preserved by God, also given the care with which the Jews are known to copy and distribute their scriptures, the logistical impossibility of revising the Torah amongst a worldwide population of Jews, etc). I've updated the following as a sort of poll as far as I can remember:
NVN, brbbs, VP, S_K