What elements are most commonly included in an exposition of faith? The "exposition of faith" (expositio fidei) or "statement of faith" is quite common. The early Church fathers often summarized an exposition of faith, and today, many Christian websites, especially those of churches, summarize a statement of faith for all to see.

What do most statements of Christian faith include? I know this is relatively subjective, but there does tend to be some consensus among the many I have seen.
Any listing of specific doctrinal statements would be, as you noted, subjective, and therefore not constructive per site guidelines.  The best answer that I can think of that would fall within site guidelines would be to give a generic answer that's applicable to all.  The approach I'm going to take is the same approach that I'd take if someone were to ask me "what should be on my resume?" while looking for a job. 



The things that should be included in a statement of faith should be those doctrines that the Church/denomination in question places importance on.  This helps people that are trying to choose a Church to know what the Church teaches, and helps them to avoid wasting their time on one that teaches false doctrine.  In general, that should include:


The Church's teaching on the nature of God
The Church's teaching on the nature of man
The Church's teaching on Scriptures (are they inerrant?  Which do we use?  Do we use the 66 books of the Protestant Bible, or do we include Apocrypha, or the Book of Mormon, or some other Scripture?)
The Church's teaching on the nature of sin, man's state, and how it affects the relationship with God?
The Church's teaching on salvation
The Church's teaching on who Christ is


Beyond that, it may also include any of the following if the Church/denomination in question deems them as central teachings


The Church's teaching on the Gifts of the Spirit (Tongues, healing, etc.)
The Church's teaching on modern/continuing revelation
The Church's teaching on prophets in the modern day
The Church's teaching on which Bible is the best (Thinking of KJV-only Churches here)

The Church's teaching on a literal account of Creation/the fall of man, etc.



In short, the included elements are entirely dependent on the teachings of the Church.  The items in the top list are those that are likely going to be important for an outsider to do an "at-a-glance" evaluation on what the Church teaches.  They're the types of things you'd want to know if you're in a new city looking for a Church to attend, or if you're shopping for a new Church.  If those all fall in line with sound doctrine, then you can move on to the items on the second list.  

These items are still important, but less agreed upon.  The first list are items that most Christians would agree on, and if something "smells wrong" in that list, it should be easy enough to write off that Church as being wrong.  The secondary items might help someone who is sure of their beliefs to find a Church that more closely aligns with his or her beliefs.