This is an interesting question.

The Catholics have a theological argument that Mary was a perpetual virgin. Most Protestants disagree, claiming that Jesus was conceived when Mary was a virgin, but that her virginity was not a concern after that. The perpetual virginity of Mary is not found in the Bible at all.

Jesus' siblings are mentioned in a couple of places in Scripture, the Gospel of Mark 6:3 and the Gospel of Matthew 13:55-56. Other mentions of Jesus' siblings occur in the epistles, including Galatians 1:19.

We have very few records of Jesus' siblings outside of the sources you wish to disregard. We have a few mentions of Jesus in Josephus and Tacitus, some Roman historians from the first couple centuries AD, but they make no mention of the rest of his family, except for one passage where Josephus mentions James as a brother of Jesus. You can read the passage here.

For an interesting read, check out this CNN piece on Jesus' siblings, it outlines the theological issues quite well.

If you want my professional opinion, yes, Jesus had siblings.

EDIT: clarity

If you disregard the gospels we have almost no information about Jesus. However, the historian Josephus has one of the only mentions of Jesus outside of the Gospels, and he mentions a brother of Jesus called James.

Absolutely. Outside of the Bible early Christians were so convinced that Jesus had siblings they even gave them a special name. Jesus's siblings were the leaders of a branch of the early church and there is a name for them identifying that branch they were called Desposyni

http://en.wikipedia.org/wiki/Brothers_of_Jesus

Eusebius has also preserved an extract from a work by Hegesippus (c.110–c.180), who wrote five books (now lost except for some quotations by Eusebius) of Commentaries on the Acts of the Church. The extract refers to the period from the reign of Domitian (81–96) to that of Trajan (98–117), and includes the statement that two Desposyni brought before Domitian later became leaders of the churches:[17]

There still survived of the kindred of the Lord the grandsons of Judas, who according to the flesh was called his brother. These were informed against, as belonging to the family of David, and Evocatus brought them before Domitian Caesar: for that emperor dreaded the advent of Christ, as Herod had done.

So he asked them whether they were of the family of David; and they confessed they were. Next he asked them what property they had, or how much money they possessed. They both replied that they had only 9000 denaria between them, each of them owning half that sum; but even this they said they did not possess in cash, but as the estimated value of some land, consisting of thirty-nine plethra only, out of which they had to pay the dues, and that they supported themselves by their own labour. And then they began to hold out their hands, exhibiting, as proof of their manual labour, the roughness of their skin, and the corns raised on their hands by constant work.

Being then asked concerning Christ and His kingdom, what was its nature, and when and where it was to appear, they returned answer that it was not of this world, nor of the earth, but belonging to the sphere of heaven and angels, and would make its appearance at the end of time, when He shall come in glory, and judge living and dead, and render to every one according to the course of his life.

Thereupon Domitian passed no condemnation upon them, but treated them with contempt, as too mean for notice, and let them go free. At the same time he issued a command, and put a stop to the persecution against the Church.

When they were released they became leaders of the churches, as was natural in the case of those who were at once martyrs and of the kindred of the Lord. And, after the establishment of peace to the Church, their lives were prolonged to the reign of Trajan. — Eusebius of Caesarea , Historia Ecclesiae, 3:20

What denomination claims Jesus had no siblings?

All of the ancient apostolic churches profess a belief in aeiparthenos Mary, ever-virgin Mary. Catholic, Orthodox, and Oriental Orthodox churches continue an ancient tradition that Jesus has no full brothers, and that Mary is ever-virgin. They may fight like cats on other issues, but in that they all seem to be in agreement.

Catholics outside the Latin rite, Orthodox, and Oriental Orthodox tend to follow the tradition from the protoevangelion of James (mid-second century) that Joseph had sons from a previous marriage before he was widowed. Many Latin-rite Catholics tend to follow a tradition from Hieronymous (Jerome, late fourth century) that the biblical word "brothers" should be interpreted as cousins and near relations. He was writing against specific arguments of a certain Helvidius.

Many modern Protestants believe that "brothers" should be interpreted as full brothers, sons of Mary. This is in contrast to the views of Martin Luther and Huldrych Zwingli, who both professed a belief in the perpetual virginity of Mary. I believe therefore that the modern line of Protestant thought probably follows from Jehan Cauvin or Calvinist thinking, but I have not traced it.

I'll just provide some reasonable doubt to this claim as the consensus here seems to be that Jesus did in fact have siblings.

In Mark 6:3 it is said:

“Is not this the carpenter, the son of Mary and brother of James and Joses and Judas and Simon, and are his sisters here with us?”

Which would seem to indicate that Jesus had brothers. Similarly in Luke 8:19-21 a crowd gathers to hear Jesus speak and he is told:

“Your mother and your brothers are standing outside, wanting to see you.”

Interestingly enough Jesus replies:

“Who are my mother and my brothers?” he asks. “My mother and my brothers are those who hear the word of God and do it.”

This use of brothers to mean 'brothers in spirit' rather than biological brothers is a common theme in the Gospels, indeed there may even be translation issues when it comes to the word brother, as the greek word for it "adelphos" can extend to distant cousins, or those with which one shares a spiritual bond.

Genesis 13:8 is an example of this

“So Abram said to Lot, “Let’s not have any quarreling between you and me, or between your herdsmen and mine, for we are brothers.”

Even though it is known that they were not brothers. Similarly in Paul's first letter to the Corinthians 15:6 reads:

“Then, he [Jesus] appeared to more than five hundred brothers at the same time, many of whom are with us still, but some have fallen asleep.”

Which clearly refers to a large crowd of believers. Now, concerning the Roman historian Josephus who mentions James as a brother of Jesus, if it is the case that Jesus had no siblings then he may be referring to one of the apostles, James or James The Lesser.

Personally I don't believe that Jesus had siblings, as there are simply to many question marks over their existence. Jesus' brothers are only mentioned in an off-hand sense, we learn nothing about them, whether they followed Jesus or not, and what became of them.

Standing at the foot of the Cross were Mary, mother of Jesus, the two other Marys—Mary of Cleophas and Mary Magdalen—and the apostle John. As he was dying, Jesus gave Mary to John. His words were “Woman, behold your son.” And to John, he said, “Behold your mother.” And from that hour the disciple took her into his home. (John 19:26-27).

If there were siblings living this may not have been necessary. Their existence is too ambiguous a question to answer definitively, but in my opinion, the lack of evidence to indicate that they did suggests that Jesus had no siblings.