That's a very tricky question which deserves some bullet points.
The scripture used during Mass and liturgical events and prayers (Benediction, Liturgy of the Hours) should always come from the Vulgate (Latin) Bible. In the United States we use the older New American Bible, with the revised edition waiting in the wings to be implemented at some future date (we'll be able to walk in the valley of the shadow of death again, yay!)
Dei Verbum (the dogmatic constitution on sacred scripture, which came out of Vatican II (the big 1960's Catholic get together)) printed at the beginning of many Catholic Bibles says this:
And should the opportunity arise and the Church authorities approve, if these translations are produced in cooperation with the separated brethren as well, all Christians will be able to use them. (Source)
So, there's a Catholic edition of all sorts of Protestant Bibles. I've got a "The Way" Catholic Edition and a "Good News" Catholic Edition and an Oxford Study Bible (With Apocrypha).
What a Catholic would look for at the start of any book is a nihil obstat (nothing stands in the way) and Imprimatur (let it be printed), meaning there is nothing in book that goes against Catholic doctrine. "Make Way for Ducklings" could qualify for a nihil obstat. It's not sign of approval, but of non-disapproval.
Frankly the translation doesn't mean a lot to Catholics since we're not the ones who are supposed to interpret the Bible, and interpretation and translation are totally different things.
But the task of authentically interpreting the word of God, whether written or handed on, has been entrusted exclusively to the living teaching office of the Church, whose authority is exercised in the name of Jesus Christ. This teaching office is not above the word of God, but serves it, teaching only what has been handed on, listening to it devoutly, guarding it scrupulously and explaining it faithfully in accord with a divine commission and with the help of the Holy Spirit, it draws from this one deposit of faith everything which it presents for belief as divinely revealed. (Ibid)
So, we don't need to shield our eyes when someone gives us a verse from the NIV or anything, we just can't assume that we know what anything means unless it's been explained authoritatively to us through the Church.
And the explanation is the eternal unchanged explanation, in the context of the entirety of scripture and in line with the consistent teaching of the Bishops.
So, if we read that Mary was the happiest of women, we know that that happiness is the happiness that can only come from knowing that she is to be the Mother of God and that the term happiness is synonymous with blessed - even though in general happiness and blessedness don't mean exactly the same thing.