Judge not?

One of the most cited verses in all of Scripture, to be sure.

And that's exactly what it says - Judge not, that you be not judged.  Matthew 7:1

What does it mean?

Let's look at other passages and contexts that pertain to judging and see if we can better understand what we are to do re judging/not judging.

Matthew 7:1-6  Judge not, that you be not judged. For with the judgment you pronounce you will be judged, and with the measure you use it will be measured to you. Why do you see the speck that is in your brother's eye, but do not notice the log that is in your own eye? Or how can you say to your brother, ‘Let me take the speck out of your eye,’ when there is the log in your own eye? You hypocrite, first take the log out of your own eye, and then you will see clearly to take the speck out of your brother's eye.
“Do not give dogs what is holy, and do not throw your pearls before pigs, lest they trample them underfoot and turn to attack you.
Luke 6:37  Judge not, and you will not be judged; condemn not, and you will not be condemned; forgive, and you will be forgiven
Romans 2:1-6,17-24, 14:10-19 Therefore you have no excuse, O man, every one of you who judges. For in passing judgment on another you condemn yourself, because you, the judge, practice the very same things. We know that the judgment of God rightly falls on those who practice such things. Do you suppose, O man—you who judge those who practice such things and yet do them yourself—that you will escape the judgment of God? Or do you presume on the riches of his kindness and forbearance and patience, not knowing that God's kindness is meant to lead you to repentance? But because of your hard and impenitent heart you are storing up wrath for yourself on the day of wrath when God's righteous judgment will be revealed.
He will render to each one according to his works:
17-24 - Now you, if you call yourself a Jew; if you rely on the law and boast in God; 18 if you know his will and approve of what is superior because you are instructed by the law; 19 if you are convinced that you are a guide for the blind, a light for those who are in the dark, 20 an instructor of the foolish, a teacher of little children, because you have in the law the embodiment of knowledge and truth— 21 you, then, who teach others, do you not teach yourself? You who preach against stealing, do you steal? 22 You who say that people should not commit adultery, do you commit adultery? You who abhor idols, do you rob temples? 23 You who boast in the law, do you dishonor God by breaking the law? 24 As it is written: “God’s name is blasphemed among the Gentiles because of you.
14:10-19 -Why do you pass judgment on your brother? Or you, why do you despise your brother? For we will all stand before the judgment seat of God; 11 for it is written,
“As I live, says the Lord, every knee shall bow to me,
    and every tongue shall confess[a] to God.”
12 So then each of us will give an account of himself to God.13 Therefore let us not pass judgment on one another any longer, but rather decide never to put a stumbling block or hindrance in the way of a brother. 14 I know and am persuaded in the Lord Jesus that nothing is unclean in itself, but it is unclean for anyone who thinks it unclean. 15 For if your brother is grieved by what you eat, you are no longer walking in love. By what you eat, do not destroy the one for whom Christ died. 16 So do not let what you regard as good be spoken of as evil. 17 For the kingdom of God is not a matter of eating and drinking but of righteousness and peace and joy in the Holy Spirit. 18 Whoever thus serves Christ is acceptable to God and approved by men. 19 So then let us pursue what makes for peace and for mutual upbuilding.

Numerous other passages (James 4:11-12, 5:19-20/Galatians 6:1/I Corinthians 4:5/I John 4:1-6/Matthew 18:15-20) proclaim the same principles as these.  I strongly urge you to look them up for yourself and ask God to explain His Word to you.

Here are some thoughts for you to consider:
1.  What is judging?  I find it helpful to look at the word originally used when these texts were penned to better understand the meaning. These passages were written in Greek and the Greek word that is most often translated as "judge"(verb) is krino. (In some New Testament translations, the English word "judge" is used for another word which would better be translated as "speak against".  I use New American Standard and English Standard Version for word studies because these translations are closest to the original documents and therefore, better preserve the intended meaning)
Krino means "to come to a decision, to pass sentence upon. to condemn or punish" and can also include the meaning of preference of one over another.
2.  This word is different from the word used in exhortation of discerning right from wrong (I John 4:1, I Corinthians 12:10) diakrino  In passages containing this word, the admonition is to distinguish between truth and error, to make a distinction between right and wrong.
3.  We Christians are clearly instructed in our responsibility to our brothers and sisters -
   - mercy (James 4:8-13)
   -distinguish between truth and error...righteously (John 7:23,24; I Corinthians 12:10)
   - self-examination (Matthew 7:1-5, I Corinthians 10:12)
   - restoration of those in sin (Galatians 6:1, James 5:19,20)
   - things are to be handled privately, gently, with love (Matthew 18:15-17)
4.  Singling out one sin over another is dangerous.  Without humility and self-examination, it will inevitably result in hypocrisy, not to mention alienation from the very ones in need of restoration.
5.  However, silence regarding the truth of what is sin is not "holier". Keeping quiet is not always a means of making peace; instead it may be a cowardly attempt to avoid personal rejection.  This will not result in the restoration of a brother or sister; therefore this action falls short of what Jesus told us to do - Love our neighbor as ourselves.  Because Love does no wrong to a neighbor.  And to allow one to blindly remain on a course that falls short of God's plan is not love (Matthew 22:39, Romans 13:10, James 5:19,20)

Judge for yourself what the Bible teaches about judging.