First of all I am NOT saying the Bible translations that support a Rapture interpretation in II Thess. 2:3 are the best Bible translations PERIOD.  They may well be, I'm just not saying it so wanted to head off anyone counter-posting that another translation was "better".  Just that these were the Bible translations that could be said to best support a Rapture before the Second Coming based on II Thess. 2:3.

Nor am I saying that these Bible translations are the best or most accurate translation of the original language for II Thess. 2:3.  Again, they may well be.  Nor am I saying that the word "departing" can also mean spiritually, such as "departing from the faith" instead of physically such as "departing from this earth" as in the Rapture.

Research was done using:  http://www.studylight.org/

Second of all, notice that all the supporting translations are pre-1600's translations, Geneva Bible (1587), Miles Covendale (1535), and Tyndale (1525).  In particular the latest is the Geneva Bible that was widely used by the Pilgrims and other groups that came to America to escape religious persecution.  Of all the translations available at studylight.org, there are 3 that are supportive as mentioned above, 6 that are neutral, (depends on your definition of apostasy), and 31 that are not supportive. 

Because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it.  Matthew 7:14

Third, several web sites that state they are providing you the Geneva Bible translation, are not, as witnessed by their version of II Thessalonians 2:3.  Another test is that the real Geneva Bible translation has Genesis 3:7 with breeches not aprons.  Those sites that say they are providing the Geneva Bible but are not, include at least at the time of this post:

http://bible.crosswalk.com/Commentaries/GenevaStudyBible/gen.cgi?book=2th&chapter=002

http://www.reformedreader.org/gbn/gbngenesis.htm

http://bible.christiansunite.com/gen.cgi?b=2Th&c=2

Fourth, the "New Geneva Bible" is not the Geneva Bible, nor is it based on the Geneva Bible translation.  Instead it currently contains the "New King James Version".  It just also contains copious notes in the manner of the Geneva Bible.

Does this smell a little like an orchestrated effort to hide the truth of God's word, assuming of course II Thess. 2:3 as originally inspired by God supports a rapture before the second coming?  Who would do such a thing?  Our enemy and great adversary of course. 

There is a conspiracy of her prophets in the midst thereof, like a roaring lion ravening the prey; they have devoured souls; they have taken the treasure and precious things; they have made her many widows in the midst thereof.  Ezekiel 22:25

Be sober, be vigilant; because your adversary the devil, as a roaring lion, walketh about, seeking whom he may devour:  I Peter 5:8


II Thessalonians 2:3

Supporting

Geneva Bible (1587)
Let no man deceiue you by any meanes: for that day shall not come, except there come a departing first, and that that man of sinne be disclosed, euen the sonne of perdition,

Miles Covendale (1535)
Let noman disceaue you by eny meanes. For the LORDE commeth not, excepte the departynge come first, and that that Man of synne be opened, euen the sonne of perdicion,

Tyndale New Testament (1526)
Let no ma deceave you by eny meanes for the lorde commeth not excepte ther come a departynge fyrst and that that synfnll man be opened ye sonne of perdicion


"Neutral"

New American Standard Bible
Let no one in any way deceive you, for it will not come unless the apostasy comes first, and the man of lawlessness is revealed, the son of destruction.

The Darby Translation
Let not any one deceive you in any manner, because [it will not be] unless the apostasy have first come, and the man of sin have been revealed, the son of perdition;

Holman Christian Standard Bible®
Don't let anyone deceive you in any way. For [that day] will not come unless the apostasy comes first and the man of lawlessness is revealed, the son of destruction.

The NAS Strong's Version
Let no one in any way deceive you, for it will not come unless the apostasy comes first, and the man of lawlessness is revealed, the son of destruction,

The Complete Jewish Bible
Don't let anyone deceive you in any way. For the Day will not come until after the Apostasy has come and the man who separates himself from Torah has been revealed, the one destined for doom.

Weymouth's New Testament
Let no one in any way deceive you, for that day cannot come without the coming of the apostasy first, and the appearing of the man of sin, the son of perdition, who sets himself against,


Not-Supporting

The Amplified Bible
Let no one deceive or beguile you in any way, for that day will not come except the apostasy comes first [unless the predicted great falling away of those who have professed to be Christians has come], and the man of lawlessness (sin) is revealed, who is the son of doom (of perdition),

Good News Translation
Do not let anyone deceive you in any way. For the Day will not come until the final Rebellion takes place and the Wicked One appears, who is destined to hell.

New King James
Let no one deceive you by any means; for that Day will not come unless the falling away comes first, and the man of sin is revealed, the son of perdition,

The New Revised Standard Version
Let no one deceive you in any way; for that day will not come unless the rebellion comes first and the lawless one is revealed, the one destined for destruction.
 
The KJV Strong's Version
Let no man deceive you by any means: for that day shall not come, except there come a falling away first, and that man of sin be revealed, the son of perdition;

The Holy Bible, New International Version®
Don't let anyone deceive you in any way, for that day will not come until the rebellion occurs and the man of lawlessness is revealed, the man doomed to destruction.

GOD'S WORD
Don't let anyone deceive you about this in any way. That day cannot come unless a revolt takes place first, and the man of sin, the man of destruction, is revealed.

Young's Literal Translation
let not any one deceive you in any manner, because -- if the falling away may not come first, and the man of sin be revealed -- the son of the destruction,

The Wycliffe Bible (1395)
No man disseyue you in ony manere. For but dissencioun come first, and the man of synne be schewid, the sonne of perdicioun,

Daniel Mace New Testament (1729)
don't be led into any mistake, because the previous rebellion does not yet appear, nor the man of sin throw off the disguise, that offspring of perdition:

Wesley's New Testament (1755)
Let no man deceive you by any means, for that day shall not come, unless the falling away come first, and the man of sin be revealed, the son of perdition,

Updated Bible Version 1.9
let no man beguile you in any wise: for [it will not be,] except the falling away comes first, and the man of lawlessness is revealed, the son of perdition,

J.P. Green's Literal Translation
Do not let anyone deceive you in any way, because that Day will not come unless first comes the falling away, and the man of sin is revealed, the son of perdition,

Holy Bible, The New Living Translation
Don't be fooled by what they say.For that day will not come until there is a great rebellion against God and the man of lawlessness is revealed – the one who brings destruction.

New Century Version
Do not let anyone fool you in any way. That day of the Lord will not come until the turning away from God happens and the Man of Evil, who is on his way to hell, appears.

The Douay-Rheims Bible
Let no man deceive you by any means: for unless there come a revolt first, and the man of sin be revealed, the son of perdition

World English Bible
Let no one deceive you in any way. For it will not be, unless the falling away comes first, and the man of sin is revealed, the son of destruction,

International Standard Version
Do not let anyone deceive you in any way, for that day cannot come unless the rebellion takes place first and the man of sin, who is destined for destruction, is revealed.

The Bishop's Bible (1568)
Let no man deceaue you by any meanes, for [the Lorde shall not come] excepte there come a fallyng away first, & that that man of sinne be reuealed, the sonne of perdition,

The American Standard Version
let no man beguile you in any wise: for [it will not be,] except the falling away come first, and the man of sin be revealed, the son of perdition,

Contemporary English Version
But don't be fooled! People will rebel against God. Then before the Lord returns, the wicked one who is doomed to be destroyed will appear.

The King James Version (Authorized)
Let no man deceive you by any means: for that day shall not come, except there come a falling away first, and that man of sin be revealed, the son of perdition;

The Revised Standard Version
Let no one deceive you in any way; for that day will not come, unless the rebellion comes first, and the man of lawlessness is revealed, the son of perdition,

Holy Bible: Easy-to-Read Version
Don't let any person fool you in any way. {That day of the Lord will not come} until the turning away {from God} happens. And {that day will not come} until the Man of Evil appears (comes). That Man of Evil belongs to hell.

The J.B. Rotherham Emphasized Bible
That no one may cheat, you, in any one respect. Because that day will not set in - except the revolt come first, and there he revealed the man of lawlessness, the son of destruction,

The Bible in Basic English
Give no belief to false words: because there will first be a falling away from the faith, and the revelation of the man of sin, the son of destruction,

Holy Bible, English Standard Version
Let no one deceive you in any way. For that day will not come, unless the rebellion comes first, and the man of lawlessness is revealed, the son of destruction,

Peshitta - Lamsa Translation
Let no man deceive you by any means: for that day shall not come, unless it is preceded by a rebellion, and the man of sin be revealed as the son of perdition,

Webster's Bible Translation
Let no man deceive you by any means: for [that day shall not come], except there come a falling away first, and that man of sin be revealed, the son of perdition;

New Life Bible
Do not let anyone fool you. For the Lord will not come again until many people turn away from God. Then the leader of those who break the law will come. He is the man of sin.

King James Version (1611)
Let no man deceiue you by any meanes, for that day shall not come, except there come a falling away first, and that man of sinne bee reuealed, the sonne of perdition,