Is there, or was there, a Christian denomination that believes, or believed, that Jesus Christ was "just a normal human"?

Yes, there have been several "denominations" that have believed Yeshua was a man. However, because a large majority of the church believes this is a heresy (and that to deny the trinity causes one to be subjected to eternal torture), this is not the most popular position.

The very first Unitarians were probably the Ebonites, or "the Poor Ones". They were vegetarian, denied the virgin birth, believed Paul to be a false apostle, and the only manuscripts they used were the Hebrew Scriptures and a Hebrew version of Matthew. They are considered the first Christians by most secular scholars, and they are mentioned several times by the early church writers.

In the third century there was Paul of Samosata. Not much is known about him because all his writings have been destroyed. Most of what we know comes from Eusebius of Caesarea. Eusebius quotes a letter which says:

Whereas he has departed from the rule of faith, and has turned aside after base and spurious teachings, it is not necessary,—since he is without,—that we should pass judgment upon his practices: as for instance in that although formerly destitute and poor, and having received no wealth from his fathers, nor made anything by trade or business, he now possesses abundant wealth through his iniquities and sacrilegious acts, and through those things which he extorts from the brethren, depriving the injured of their rights and promising to assist them for reward, yet deceiving them, and plundering those who in their trouble are ready to give that they may obtain reconciliation with their oppressors, ‘supposing that gain is godliness

So rather than offer any argument against Paul's doctrine, the writer simply says they do not feel it necessary to attack Paul's character...but they're gonna do it anyways. Unfortunately, Eusibius doesn't offer any quotes from Paul, but some of his writings have been preserved.

After the Nicea Council, the Catholic Church basically dominated all intellectual thought. Issac Newton is believed to be an Arian, though it's hard to tell. He was definitely nontrinitarian, and had to hide his beliefs to avoid the death penalty.

During the Reformation, a few men saw the opportunity to bring the issue up again. Although it's unclear what Michael Servetus believed, he is definitely worth mentioning. Servetus wrote a few books about his theology, and he was a key player in the Reformation. His views were considered heresy by both the Catholic and the Protestant churches. In 1553, he was arrested and condemned to death by John Calvin. Calvin wanted Servetus to be beheaded, but the council that held his trial denied this request; instead, they burned him at the stake while his books provided the fuel for the flames.

Also around this time was Fausto Sozzini, from which the label Socinianism comes from. Scozzini denied that Messiah preexisted, though he did believe in the virgin birth. His followers became know as Socinians until Henry Hedworth introduced the term "unitarian" in 1673.

During the Enlightenment in the late 1700's, there was a man named Joseph Priestley, who is considered the father of modern chemistry. He wrote a book called A History of the Corruptions of Christianity. Priestley helped form the first Unitarian churches in England and was very outspoken about his beliefs. He is well known for his accomplishments in the secular world, but he considered these things hobbies and likened himself as a theologian above all else. In 1791, his home and church in London was burned to the ground, so he spent the rest of his days in the United States.

Thomas Jefferson was a big fan of Priestley, and he wrote many letters to him. He also wrote to John Adams about Priestley, in which he said:

You are right in supposing, in one of yours, that I had not read much of Priestley's Predestination, his no-soul system, or his controversy with Horsley. But I have read his Corruptions of Christianity, and Early Opinions of Jesus, over and over again; and I rest on them, and on Middleton's writings, especially his Letters from Rome, and To Waterland, as the basis of my own faith. These writings have never been answered, nor can be answered by quoting historical proofs, as they have done. For these facts, therefore, I cling to their learning, so much superior to my own.

Jefferson is also known for famously taking a razor blade to a King James bible, stripping the words of Yeshua and compiling them together into what has become known as The Jefferson Bible.

He was so happy about his work, he wrote to John Adams saying:

In extracting the pure principles which he taught, we should have to strip off the artificial vestments in which they have been muffled by priests, who have travestied them into various forms, as instruments of riches and power to themselves. We must dismiss the Platonists and Plotinists, the Stagyrites and Gamalielites, the Eclectics, the Gnostics and Scholastics, their essences and emanations, their logos and demiurges, aeons and daemons, male and female, with a long train of … or, shall I say at once, of nonsense. We must reduce our volume to the simple evangelists, select, even from them, the very words only of Jesus, paring off the amphibologisms into which they have been led, by forgetting often, or not understanding, what had fallen from him, by giving their own misconceptions as his dicta, and expressing unintelligibly for others what they had not understood themselves. There will be found remaining the most sublime and benevolent code of morals which has ever been offered to man. I have performed this operation for my own use, by cutting verse by verse out of the printed book, and arranging the matter which is evidently his, and which is as easily distinguishable as diamonds in a dunghill. The result is an octavo of forty-six pages, of pure and unsophisticated doctrines.

In recent times, there are the Unitarian Universalist Association, the Biblical Unitarians, the Christadelphians, Douglas J. Del Tondo from Jesus' Words Only, and some guy that runs the Trinity Delusion, to name a few. The UUA is more of a spiritual new-age movement, so I wouldn't recommend them for serious biblical studies. We may differ on a few things, but we basically all agree that the earth is populated with humans, God made and loves humans, and the only true God sent His human son, Yeshua the Messiah, to be the savior of the world.

Historically, there have been a number of sects that denied the divinity of Jesus, claiming that he was a man, and nothing more.*

In the first few centuries of Christianity, most of these groups held the Christiological heresy (from the point of view of mainstream Christianity) called Adoptionism, also known as dynamic monarchianism. Its basic tenet is that Jesus was merely a man, and that he became the Son of God by adoption at some historical moment: generally the Baptism in the Jordan, at the Resurrection, or the Ascension.

The most famous adherents of this heresy were Theodotus of Byzantium and Paul of Samosata. This was also the theory, apparently, of the Ebionites, who were a group of Jews living in the first and second century, who considered Jesus the Messiah, but not the natural Son of God (as orthodox Christians do).

These early sects have long since died out; however, in later centuries, there have been many individuals who have considered Jesus to be a great moral teacher, or a wise philosopher, but not God. This, for example, is generally the attitude of Deism (a philosophical position toward religion that became common in the Enlightenment period, roughly 1715-1789, ending with the French Revolution) toward Jesus.

Perhaps the denomination that comes nearest to an explicit denial of Jesus’ divinity is Unitarianism. Historically, Unitarianism professes an explicit denial of the dogma of the Holy Trinity. (In this sense, the Unitarians re-proposed a doctrine similar to Monarchianism. Historically, Monarchianism—the denial of the Trinity—has two possible Christological implications: either Adoptionism, as described above, or Modalism or Patripassianism, which does not deny Jesus’s divinity, but denies that Jesus’s Person is distinct from the Father.) As a general tendency, Unitarians have tended to downplay the supernatural aspects of Jesus’ life and ministry, so they generally do not acknowledge his Divinity, in the orthodox sense. (The denomination does not impose a definite creed, and so there is a wide variety of beliefs and opinions.)

* Attentive readers will observe that I left out the most important historical denial of the divinity of Christ: Arianism. The reason is that Arianism is principally a Trinitarian heresy; that is, Arius and his followers denied that the Word—the Second Person of the Trinity—is God like the Father. They did not, however, deny the supernatural character of the Incarnation, nor that Jesus was more than merely a man. (In fact, their Christology was closer to that of Apollinaris of Laodicea, which tended to deny Jesus’ full humanity.)