According to 1 Corinthians 11:14, it is disgraceful for men to have long hair:
Does not nature itself teach you that if a man wears long hair it is a disgrace for him?
Why, then, is Jesus often depicted with long hair?
Even if the premise that Christ had longer hair is true, it would not matter as that is not the point of this passage. If it is read in context i.e. read the chapter before and after, it is clear that Paul is talking about how Jewish customs and how even though they are no longer necessary due to Christ's sacrifice, they should still be observed if you are causing your brother to stumble:
"So, whether you eat or drink, or whatever you do, do all for the glory of God. Give no offense to Jews or to Greeks or to the Church of God" - 1 Corinthians 10: 31-32
Then he goes on in the start of Chapter 11 to talk about the custom of women covering their head to worship and men uncovering their head to worship and why that custom was in place: because angels needed to cover their head out of reverence to God. I'm not a Jewish custom expert but I do know that the point of this passage was not to show that it is disgraceful for men to have long hair but to show that you must respect the customs of the people you are around in church. This is shown by the ending phrase of that section:
"If anyone is inclined to be contentious, we have no such practice [of head covering], nor do the churches of God. - 1 Corintians 11:16
It is important to always read God's word in context as it was meant or else you run the danger of missing the point.
Hope this helps :)
Being as there is no image of Jesus that has any historical credibility, the question is based on a faulty premise. We simply do not know what Jesus' hair looked like.
The paintings to which you allude tend to be those painted by the European masters in the 16th & 17th Centuries. At the time, it was fashionable for men to have longer hair, and thus it was not "a disgrace".
A lot of good info here, but also some mistaken assumptions. During the Renaissance, when so many portraits of Jesus were made, some men had long hair, some short. Many cropped their hair close to try to curb lice. Some high society men wore long-haired wigs. Yet the vast majority of Jesus portraits made then depict him with long hair. Since Jesus was born in a stable and raised as a carpenter, he certainly wasn't of the upper classes, so it's puzzling that he would have been depicted with long hair. However, the artists also almost universally depicted Jesus with a halo, which he clearly did not have. If he had a halo, why would the chief priest have said, "If you are the son of God, tell us!" (Luke 22:67) Putting a halo on a figure was a pagan artistic license predating Jesus, used to depict heroes and other figures considered sacred, such as the Buddha. Perhaps painting him with long hair pleased the upper-class folks who were, after all, paying for the paintings.
Another comment said 'angels have long hair.' There is no scriptural backing for that statement. What the scriptures do say about angels is, 1. There are "myriads of myriads" of them (a myriad equals 10,000, so hundreds of millions). 2. They predate humans. (Job 38:7) 3. They are always depicted as powerful (2 Kings 19:35), masculine or neutral, never as women or cherubic babies (Revelation 19:10).
What do the scriptures say about hair length? David's son, Absalom, cut his hair once a year (2 Samuel 14:26) but if that were the norm, why was it even mentioned? The command at Leviticus 14:26 to not shave the sides of the head - which rastafarians have misunderstood to mean never cutting one's hair - was in fact an injunction against the weird haircuts Israel's neighbors sported to honor their gods. (Jeremiah 9:25, 26) Israelite men displayed mourning by ignoring their hair and beard, letting both straggle. (Job 1:20; 2 Samuel 19:24) Israelite women displayed mourning by cutting their hair off. (Isaiah 3:24) Notice the role reversal there: normally men kept their hair and beard short, and normally women let their hair grow long. As another commenter pointed out, nazirites - Jews who had taken a special vow of service to God, or been appointed to some special duty by God, like Samson - went against the norm by leaving their hair long, but Jesus was not a nazirite.
Now, as to Paul's words about hair: In 1 Corinthians 11:3, he's talking about the headship principle: 'the head of the woman is the man; the head of the man is the Christ; the head of the Christ is God.' In verse 4 he immediately moves into the discussion of covering one's head. "Every man who prays or prophesies with something on his head shames his head." Note that this was NOT a nod to Jewish custom of that day; it was flying in the face of custom. As Paul himself says in 2 Corinthians 3:14, "to this very day during the reading of the book of the Law, the same veil remains unlifted." Commentator Adam Clarke says of this: "Here is an evident allusion to the conduct of the Jews in their synagogues: when they read the law they cover their whole head with a veil, which they term the tallith, and this voluntary usage of theirs, the apostle tells us, is an emblem of the darkness of their hearts." So Paul was telling Christian men to NOT cover their heads at Christian meetings in imitation of Jewish custom. (Artwork of Jesus teaching or praying with his head covered is drawn from Jewish tradition, and Jesus hated Jewish tradition - Matthew 15:6)
Back to the account at 1 Corinthians 11. In verse 6 he says a woman is disgraced by having her hair cut off; Verses 14 and 15 say, "Does not even nature itself teach you that if man has long hair, it is a shame to him? But if a woman should have long hair, it is a glory to her; for her hair is given to her in place of a veil." That's pretty clear. Which brings us back to the question: Why is Jesus depicted with long hair? Could it be that those Renaissance artists were influenced, either by the popes of their day or by Satan, to make Jesus look weak, ineffectual or effeminate? The Borgias, one of whom may have modeled for a portrait of Jesus, certainly had good reason to hope Jesus was a wimp.
It is important to remember that Jesus is God's Word in the flesh, thus an eternal being. Although He entered into human consciousness during a period in history, He did not live in that period alone. The Son of God was always present even before the foundations of the earth and forevermore. If Jesus were portrayed with a certain haircut, it would put Him in a period. The portrait of Jesus cannot be presented with a hair-style or a haircut because He is an eternal being: the same reason why angels always have long hair.