In addition to the Verse from surat al Hujurat (49:11) which was already mentioned by azam and pedro. I would like to recall the story of the Prophet Musa/Moses (Peace be upon him and al-Khidr which is mentioned in surat al-Kahf (18:60-82):
To sum up the story briefly, Prophet Musa (Peace be upon him) followed a learned man called Al-Khidr to get guidance. He kept seeing Al-Khidr do actions that to Musa seemed wrong and Musa would speak up and point out that they were wrong. At the end, it turned out that Al-Khidrs intention had been good all along and though his actions seemed wrong he was actually doing them to benefit the people. This shows us that there are things of which we have no knowledge and should not think that we do and therefore shouldn't judge.
For example judging others (being suspicious) is mentioned in Muwatta' al Imam Malik and both Sahihs:
Abu Huraira reported Allah's Messenger (ﷺ) as saying:
Avoid suspicion, for suspicion is the gravest lie in talk and do not be inquisitive about one another and do not spy upon one another and do not feel envy with the other, and nurse no malice, and nurse no aversion and hostility against one another. And be fellow-brothers and servants of Allah.
and also some ahadith provide stories of people who judged others and went to hell because they judged their intentions (something what we can't judge foresee) or showing that prejudice can lead to grave mistakes. So we could say that man does not have the authority to judge another in matters of faith as he cannot see into the hearts of others therefore Allah enjoins that He be the Judge of such affairs.
Also here are some statements on the matter:
O'mar ibn al-Khattab (May Allah be pleased with him) said (My own translation so take it carefully):
ولا تظنن بكلمة خرجت من أخيك المسلم إلا خيرا ، وأنت تجد لها في الخير محملا
(From Tafsir ibn Kathir)
Do always think good/kindly for any word that your Muslim brother spoke out if you could find a good and nice sense (or even the smallest carrier to make it sound nice)!
Hamdun al-Qassar, one of the great early Muslims, said:
"If a friend among your friends errs, make seventy excuses for them. If your hearts are unable to do this, then know that the shortcoming is in your own selves [ibid]"
And the words of Imam Jafar as-Sadiq
"If you find see something you don’t like in a brother, try to find 1-70 excuses for him. And if you can’t find an excuse, say "There might be an excuse, but I don’t know it." "
Al-Dhahabî, speaking about the mistakes of the scholars, said the following: [Siyar al-A`lâm al-Nubalâ' (14/374)]:
If we were to discredit every person who made mistake in judgment or declare those people as innovators – people who are essentially of good faith and sincerely seek the truth – then scarcely would any of our scholars be spared.
And just as an addition, as i think one could say a lot more on this topic: Muslims are asked not to judge unless they would have clear proofs, and try to do their best to judge fairly and leave the final judgment to Allah.
Well i think it would be possible to add more information or elaborate a better answer if you provide us more information on what you'd like to focus on and what you mean by judging others!
My other references:
1 , 2 ,3
And Allah knows best!