Which is the "correct" bible for Catholics?

The original Douay-Rheims Bible is the most doctrinally "correct" Catholic study Bible and English translation because:

1. It is translated from the Latin Vulgate, with comparisons to the original languages; the 4th Session of the Council of Trent on the Canonical Scriptures authorized the Vulgate as the official translation of the Church:

   But if any one receive not, as sacred and canonical, the said books entire with all their parts, as they have been used to be read in the Catholic Church, and as they are contained in the old Latin vulgate edition; and knowingly and deliberately contemn the traditions aforesaid; let him be anathema.

2. The translation and commentary emphasize Catholic doctrine against the Protestant and other heresies.
3. It is free from error.
4. It is the first authorized Catholic, Modern English translation of Holy Scriptures; thus, it has great historical significance, withstanding the "test of time."

The Catholic Answers site has a good article on Bible selection. The article gives good general information about literal vs dynamic, and discusses a number of specific translations. While suggesting each person should choose according to their judgment, they do warn about versions that may be biased and suggest an appropriate choice.

We recommend staying away from translations with unconventional renderings, such as the TEV, and suggest using the Revised Standard Version- Catholic Edition. This is a Church-approved version of the RSV that has a few, minor changes in the New Testament. It has been reissued by Ignatius Press under the title The Ignatius Bible (available from Catholic Answers in both hardcover and paperback formats)

Most Catholics will probably want to have at least one Bible which contains the Deuterocanonical books and has official approval for use in the Church.

There is anecdotal evidence that Bibles like the ones in the picture on this page, apparently a King James version (KJV) printed for the Gideons, are strongly disliked by some Catholic teachers. While some (mostly Protestants) think the KJV is a very good or even the only reliable version and others have a low opinion of it, these opinions are mostly a matter of individual taste.

Back in the early 1600's there were three relatively new translations, the Douay-Rheims, the Geneva, and the King James. The Geneva was either loved or hated because it had extensive notes which discussed doctrinal issues. The King James gradually became the Bible of choice for most Protestants, and at that time only the Douay-Rheims was recommended for Catholic use.

According to Jayarathina Madharasan's answer:

The correct bible that a Catholic is supposed to use is the Latin Vulgate Bible. That is the official bible of the Catholic Church. That is the one which is used in papal masses.

Actually, we have not used Latin Lectionaries (that's the book of Scripture we use in Liturgy) in any widespread sense since the early 60's when it was switched to vernacular. Of course the Papal masses are different because they are done at the Vatican, but that is rare (unless you attend Traditional Latin Mass, which is perfectly fine but very uncommon relative to Masses in the Vernacular).

In the US, our Lectionary is based off a heavily modified version of the New American Bible (the normal NAB, and even the NABRE, do not have Vatican approval without revisions, owing to inclusive language and other factors).

As far as private reading, a great many are approved, but off the top of my head here are some of them:

• RSV-Catholic Edition (CE)
• RSV-2ND CE
• NRSV-CE
• NAB-revised edition
• Douay Rheims-Challoner Revision
• Knox Version

I know there are more, but those are probably the most widely used (with Knox being the least used among them despite the beautifully written translation).

For study, most Catholics use either the RSV-CE or RSV-2CE, as they are more readable than the Douay Rheims but also very accurate from the original languages.

For those who can read Latin, they do sell parallel Bibles with the Douay Rheims and either the Clementine Vulgate or the New Vulgate. But those are rarely used by the Laity.

In addition to Jayarathina's answer for the United States, the Catholic Bishops' Conference of England & Wales lists

For use in the Liturgy (that is, at Mass):

Revised Standard Version
Jerusalem Bible
New Jerusalem Bible*
New Revised Standard Version*
Good News — may be used for Masses with Children

Grail Psalter (1963)
Grail Psalter (revised 1993)*

For the Divine Office:

Jerusalem Bible
Knox Bible
New English Bible
Revised Standard Version
Good News

The Grail Psalter (1963) is used for the Psalms. Canticles are taken from:
Grail Psalter
Jerusalem Bible
Revised Standard Version

*These versions may only be used for individual local celebrations and may not be used to produce a Lectionary (full set of readings)

In England & Wales, the usual translation used is the Jerusalem Bible, but the above versions are permitted in their various uses. In the Personal Ordinariate of Our Lady of Walsingham, the only approved translation is the Revised Standard Version and its use is mandated in both the Ordinariate Use and the Novus Ordo celebrated by the Ordinariate (although in the latter, the Grail Psalter must be used).