Can Muslim men have long hair?

Yes. The Prophet Muhammad ﷺ himself had hair that reached his shoulders at times, so long hair for men is allowed and even seen as a Sunnah by some scholars. The conditions are to keep it clean and neat, and not to style it in ways that imitate women. Short hair is equally fine.

The Prophet's hair

Anas said: "The hair of the Prophet ﷺ used to hang down up to his shoulders" (Sahih al-Bukhari 5903). In another narration, he described it as reaching "till between his shoulders and his earlobes" (Sahih al-Bukhari 5905).

His hair length changed at different times, sometimes shorter, sometimes longer. Scholars conclude that both long and short hair are allowed for men. See Is it okay to cut my nails at night?

Is long hair a Sunnah?

Some scholars say growing hair like the Prophet ﷺ is a Sunnah you're rewarded for if your intention is to follow him. Others say hairstyles follow local custom, so choosing short or long hair is simply a personal preference. Either way, there's no sin in short hair or in long hair.

The conditions

Keep it clean and cared for. Islam values cleanliness and looking presentable.
Don't imitate women. The Prophet ﷺ "cursed those men who are in the similitude (assume the manners) of women" (Sahih al-Bukhari 5885). Scholars apply this to styles clearly seen as feminine in your culture.
Avoid half-shaved styles where part of the head is shaved and part left long, which many scholars discourage.

Ponytails, buns and braids

Tying long hair back is generally fine. Scholars differ on man buns and braids: some say they're acceptable if they're common among men locally, while others consider them too close to women's styles. Use your judgment based on your culture.

Long hair and wudu

For wudu, you only need to wipe over part of your head; you don't need to wet all your hair. For ghusl, water must reach the roots, so loosen tight styles if needed. For other grooming questions, see Do I have to grow a beard right away? and Can Muslim men wear gold rings?

Key points

Long hair is allowed for Muslim men.
The Prophet's ﷺ hair at times reached his shoulders.
Keep it clean and neat.
Avoid styles that imitate women.

Tip: If you're growing your hair to follow the Sunnah, make that your intention. Something as simple as a hairstyle can become an act of love for the Prophet ﷺ.