Do all Christians believe that Jesus is the son of God? Do any
branches of Christianity simply follow Jesus' teachings, without
believing him to be divine?

Some Unitarians follow Jesus's teachings, but do not believe that Jesus is divine.

Here's a statement about Jesus from the Unitarian Universalist Association:

http://www.uua.org/aboutuu/uufaq.html#jesus

Your answer depends on your definition of Christian. I am not aware of
any substantial organized branches of Christianity that do not assert
the divinity of Jesus, but surely there are some people who would
self-identify as Christian without believing he was divine. There are
certainly many religious people who believe in the greatness of Jesus
and follow his teachings without believing him to be divine, for
example Muslims and some Unitarian Universalists. Neither religion
claims to be Christian, although the roots of Unitarian Universalism
are in Christianity.

It seems that the United Church of Christ is even unclear as to
whether they themselves should regard Christ as divine.  See:

www.ucc.org/synod/resolutions/gs25-17.pdf

or (if you don't have a pdf reader)

http://72.14.203.104/search?q=cache:vIosf4MUaE8J:www.ucc.org/synod/resolutions/gs25-17.pdf+non+divinity+of+Jesus+Christianity&hl=en&gl=us&ct=clnk&cd=8&client=firefox-a

It is a given that when a believer is Christian, that person must
accept Christ as a divine being. However, if you are talking about the
more radical or different movements that place themselves under the
umbrella of Christianity in general, it is acknowledged that they
exist. However, these are not accepted into the mainstream types of
Christianity (like Catholicism and Evangelical Christianity), and more
often than not would be considered cults.

Jesus Christ is divine in that he is the son of Almighty God, whose
personal name is Jehovah [ Exodus 3; 13-15 & 6;3] . Jesus was his
Father's very first creation, before the universe, stars, planets,
angels, the earth, animals or man. Proverbs 8; 22-31 [22 ?Jehovah
himself produced me as the beginning of his way, the earliest of his
achievements of long ago. 23 From time indefinite I was installed,
from the start, from times earlier than the earth. 24 When there were
no watery deeps I was brought forth as with labor pains, when there
were no springs heavily charged with water. 25 Before the mountains
themselves had been settled down, ahead of the hills, I was brought
forth as with labor pains, 26 when as yet he had not made the earth
and the open spaces and the first part of the dust masses of the
productive land. 27 When he prepared the heavens I was there; when he
decreed a circle upon the face of the watery deep, 28 when he made
firm the cloud masses above, when he caused the fountains of the
watery deep to be strong, 29 when he set for the sea his decree that
the waters themselves should not pass beyond his order, when he
decreed the foundations of the earth, 30 then I came to be beside him
as a master worker, and I came to be the one he was specially fond of
day by day, I being glad before him all the time, 31 being glad at the
productive land of his earth, and the things I was fond of were with
the sons of men".
After his sacrifice for us, Jesus is again back in heaven, alongside
his Father. Being divine is NOT being Almighty God himself. It is
having a continuing spiritual existence.

Alanna found an interesting site.  It appears that the motion
presented to the synod wants to clarify for all times and all members
of the United Church of Christ that Jesus is God.  I wonder how the
voting went.
"United" churches  - they exist in Germany, separate of the UCC - 
have a problem with stating their beliefs.  Interesting:
http://www.stillspeaking.com/about/index.html
http://en.wikipedia.org/wiki/United_Church_of_Christ

How can that 'august' body say, let alone believe, that Jesus is God
himself. According to Ecclesiastes 9, Jesus is a creation of God [ his
father]. Almighty God, the Alpha and Omega, has ALWAYS been in
existence. To the most simple man in the street, a son can never be
his own father. Why should a loving God complicate so simple a
concept. The Bible after all is his word to us on how to live in peace
and behave. Many scriptures in just one Bible book, John, point to a
clear separation between God and his son. John 1;1`8..Jesus was sent
to explain his Father. John 4;34...Jesus was 'sent' to 'finish' HIS
[God's] work. John 5;19,30... Jesus cannot do a single thing OF HIS
OWN INITIATIVE. Then WHO's [?] initiative.
It seems that the Synod does not know its Bible.

Interestingly, none of the definitions found with a Google search
   define:christian

says anything beyond that a Christian follows the teachings of Christ.

Jesus Christ (pbuh) is not son of God or God according to Bible. For
example, in the Bible it is said the when Jesus (pbuh)ascended to
heaven He sat on the right side of God. Now if he was God then why
would he sit on his own right hand side? And where was the Holy Ghost?
Perhaps on the left handside. Then who was on the center? Also in the
Bible has been mentioned that when Jesus (peace be upon him) was dead
for 2 days and three nights or three nights and 2 days whichever is
that also mean that Holy Ghost was dead and May God forgive me for
writting this God was dead as well. So you see the Trinity doesn't
make sense. I know many Christians have their doubt about the Trinity
but they are afraid to question it. It is also so sad to see the some
Christians make fun of the some misguided Muslims moms and dads who
send their child to kill themselves and also kill others, now what
kind of example the Christians have a God who killed his son for the
others. Isn't it the same? What kind of God what would make? Mercyful?
I doubt it. What the Muslims believe God is God, Holy Ghost an Angle
and Jesus Christ (pbuh) is a prophet. A mighty prophet but still a
prophet just like Adam,David,Joseph,Moses and Mohammad (peace be upon
them all).