That is the question. You often hear it, I think aside from John 3:16 it is probably the most commonly quoted verse.
Judge not, that ye be not judged. (Matthew 7:1)
But did Jesus really mean not to judge anyone, ever? The way it is thrown around you would think so, wouldn't you? But somehow I get the feeling this isn't quite what He meant. If it was, why would He say 15 verses later to beware of people and the teachings they bring?
Beware of false prophets, which come to you in sheep's clothing, but inwardly they are ravening wolves. Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles? Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit. A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit. Every tree that bringeth not forth good fruit is hewn down, and cast into the fire. Wherefore by their fruits ye shall know them. (Matthew 7:15-20)
If He didn't want us to judge anyone, ever, why would He say we can know a tree by it's fruit? In order to discern between good and bad fruit one must make a distinction, a judgment between the two. So, obviously Jesus didn't mean for us to ignore each other's sin entirely. If that is what He meant then we have a serious problem on our hands because in many places through out the rest of the New Testament He would then be contradicted by the New Testament writers.
But now I have written unto you not to keep company, if any man that is called a brother be a fornicator, or covetous, or an idolater, or a railer, or a drunkard, or an extortioner; with such a one no not to eat. For what have I to do to judge them also that are without? do not ye judge them that are within? But them that are without God judgeth. Therefore put away from among yourselves that wicked person. (1 Corinthians 5:11-13)
Brethren, if any of you do err from the truth, and one convert him; Let him know, that he which converteth the sinner from the error of his way shall save a soul from death, and shall hide a multitude of sins. (James 5:19-20)
If we are not supposed to judge, how then are we to put the wicked away from our midst? If we are not supposed to judge, how then are we supposed to turn our brethren from their error? Clearly the Bible teaches there is some measure of judgement that is supposed to be taking place, and in fact I believe Christ clarifies the issue quite well for us.
If a man on the Sabbath day receive circumcision, that the law of Moses should not be broken; are ye angry at me, because I have made a man every whit whole on the Sabbath day? Judge not according to the appearance, but judge righteous judgment. (John 7:23-24)
He instructs us to judge righteously; the religious leaders want to kill Him because He keeps breaking the Sabbath, but He points out that the priests break the Sabbath whenever they circumcise a baby on the Sabbath. The priests are breaking on commandment in order to fulfill another. Perhaps this is why Jesus quotes Hosea 6:6 at another point?
For I desired mercy, and not sacrifice; and the knowledge of God more than burnt offerings. (Hosea 6:6)
After all, God is after our hearts. We can follow the letter of the law, but if our hearts are not in it for God what good is it? And so we must look to the heart. We are called to judge not only others, but ourselves as well. God's word is a mirror and we must come before it and allow Him to show us where we don't line up, and when teacher comes we must be sure to look at what they're saying. It is our responsibility to ourselves, and to others, to examine the lives of professing believers.