Short answer
A haircut is not allowed when it shaves part of the head and leaves other parts long (qaza'), copies the opposite gender, or copies a style that marks a non-Muslim religion or a sinful group. A normal fade or taper where all the hair is cut and blended is generally fine. Long hair is allowed for men if it is kept tidy and not styled like a woman's.
Qaza' (shaving some of the head and leaving patches of hair) is makruh. Shaving the whole head, cutting it all short, or leaving it all long are each permitted. Men styling their hair in a way specific to women is not allowed.
The four schools agree on this.
Explanation
The clearest rule comes from a hadith. The Prophet ﷺ saw a boy with part of his head shaved and part left, and said: shave all of it or leave all of it. This style is called qaza'. The four schools agree that it is disliked, and Hanafi muftis treat it seriously.
Fades. Most barbers' fades cut every hair and blend the sides into the top. Hanafi muftis generally allow this, since the whole head is cut and only the lengths differ. The problem comes when the sides or back are taken down to bare skin while the top stays long, or when a block or patch is shaved: many muftis treat that as qaza' and say to avoid it. Lines, words or patterns shaved into the hair fall under the same caution and copy fashions you are better off without.
Long hair for men. The Prophet's hair reached his earlobes at times and his shoulders at others, so long hair is a Sunnah style, not a problem. Keep it clean, combed and oiled. What is not allowed is a style that belongs to women in your culture, such as women's braids, hair clips or a woman's bun.
Other points. Shaving the whole head is permitted at any time, and it is the better choice after Hajj or Umrah. A haircut that copies a religious style of another faith, or the trademark look of a criminal gang, is not allowed because of imitation. Women's hair questions are in the women section. For hair colour, see dyeing your hair.
The evidence
Sunan Abi Dawud 4195
Graded sahih... احلقوه كله أو اتركوه كله ...
"Shave all of it or leave all of it."
Forbids shaving part of the head and leaving part, which is qaza'.
Sahih al-Bukhari 5921
Sahih... نهى عن القزع ...
"He forbade qaza'."
The general prohibition of qaza'.
Sunan Abi Dawud 4163
Graded hasan sahih... من كان له شعر فليكرمه ...
"Whoever has hair should look after it well."
Long or short, hair should be kept well groomed.
Where the ruling is recorded
- al-Fatawa al-Hindiyya, Kitab al-Karahiyya, chapter on circumcision, hair and nails. Defines qaza' and states that it is disliked.
- al-Durr al-Mukhtar with Radd al-Muhtar, Kitab al-Hazr wa al-Ibaha. On hair styles and imitation of women.
- al-Majmu' (Nawawi), Kitab al-Taharah, chapter on the siwak and the practices of the fitrah. Nawawi on qaza' being disliked.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.