Let's look at the passage in its context:
MATTHEW 7:1-5:
"Judge not, that ye be not judged. For with what judgment ye judge, ye shall be judged: and with what measure ye mete, it shall be measured to you again. And why beholdest thou the mote that is in thy brother's eye, but considerest not the beam that is in thine own eye? Or how wilt thou say to thy brother, Let me pull the mote out of thine eye; and behold, a beam is in thine own eye? Thou hypocrite, first cast out the beam out of thine own eye; and then shalt thou see clearly to cast the mote out of thy brother's eye."
Clearly, it is hypocritical judgment that this Scripture condemns. (Look at verse 6, and 13-15 to see that Christ actually instructs them to make judgments!) A hypocritical judgment is judging something for something of which you are also guilty - LIKE TELLING ME NOT TO JUDGE WHEN YOU ARE JUDGING ME! This passage means the opposite of what hypocrites often interpret it to mean! Jesus' point is for hypocrites to pluck the beam of sin out of their own eye so that they can see clearly to cast the mote out of their neighbor's eye.
Let's look at some other Scriptures...
JOHN 7:14: "Judge not according to appearance, but judge righteous judgment."
LUKE 12:57: "Yea, and why not even of yourselves judge ye not what is right?"
PSALM 37:30: "The mouth of the righteous speaketh wisdom, and his tongue talketh of judgment."
PROVERBS 31:9: "Open thy mouth, judge righteously, and plead the cause of the poor and needy."
LUKE 17:3: "Take heed... If thy brother trespass against thee, rebuke him; and if he repent, forgive him."
