What are the most prominent christologies in all of Christendom?

Approximately 97% of Christians belong to Trinitarian denominations, so it's a reasonable view that there are no other prominent Christologies at all. However let's ignore that argument, and consider the most prominent ones after excluding Trinitarianism.

Most of them are associated with specific denominations. For example the Latter-Day Saints and the Jehovah's Witnesses have their own distinctive Christologies, and both have around 15 million adherents. Oneness Pentecostals account for another 15 million or so. After that the numbers drop sharply, with Unitarians and Christadelpians probably having fewer than a million adherents each.

Unitarian Subordinationism - Sometimes simply called "Subordinationism," it is thought that this view may have actually been the dominant view of the Eastern Fathers until the Arian controversy. (Including Origen, Eusebius and other famous thinkers). In this view, Jesus is seen as co-eternal and co-creator alongside the Father. One may even say He is "consubstantial." However, He is either seen still as being lower than the Father in His nature or at least eternally dependent on the Father for all things. The Spirit, likewise, is either dependent on the Father or on the Father and Son from eternity and at least functionally subordinate to the Son if not in His nature. There are many Bible verses which the early Fathers used to support this position. It seems to be the closest view to Trinitarianism which is not a full blown Trinitarian viewpoint.

Arianism- The belief that Jesus was the first creation of the Father and pre-existed all other things. He is said, however, to have had a beginning in this Christology. Usually He is seen as the highest ranking angel (as in JW theology) or simply in a category all His own which is higher than angels but lower than the Father. The Holy Spirit is usually relegated to be simply "the power of God in action" or something else described in a very similar manner, and not seen as a personal manifestation of God.

Tritheism - The belief that there are simply 3 gods; Father, Son, and Holy Spirit. They are not personal manifestations of the One God, but are as separate as 3 people would be. However, they are seen as united in purpose. This is seen in Mormon theology although it is very possible to believe in a tritheism which is very dissimilar from Mormonism.

Humanitarian Unitarianism - This view is very broad. The underlying denominator to this view is that Jesus was only a human being. No more, no less. Some versions of this are Adoptionism (Jesus was "adopted" as the Son of God, at His baptism perhaps), or just something along the lines of "Socinianism" (Jesus is just a human who had a special relationship with God). Whatever the details are, the key is that Jesus is ultimately seen to be only a man.

It is also worthy to note that there are many different kinds of Trinitarianism. Many Trinitarians were considered heretics later on down the line after Nicaea. Usually the reason for this was that even though they believed Jesus/The Holy Spirit were God, they denied that He had a human and divine nature (monophysitism) or they said that He was 2 persons with 2 natures (Nestorianism), or even still they denied in some way that He was 100% God and 100% man (Apollinarianism). Today, the two largest groups of Trinitarians in the west are "Latin Trinitarians" and "Social Trinitarians." The Orthodox church of the East adheres to a Trinitarianism which is described as the "monarchy of the Father" view.

I'm sorry I know you asked for 10 but I really can't think of any more prominent Christologies.