Did Jesus Claim To Be God?

Have a discussion about Jesus with almost any secular person (meaning they are uncommitted to any ideology) and such a person will usually at least acknowledge that Jesus was an important historical figure if not a "good" man.  But ask them if Jesus claimed to be God and you may be surprised at the responses.
Jesus being called "lord" in the Bible is not enough to prove He claimed to be God; for the word "lord" often means simply "master", "teacher", or "rabbi" -- a title of respect sometimes even used of mere men (ref).
Before we get into the verses that prove Jesus claimed to be God, let's look at this "great proposition".  In chapter 8 of "Evidence That Demands A Verdict" (ETDAV) we are given 8 answers to the proposition; IF GOD BECAME MAN, THEN WE WOULD EXPECT HIM TO:

1. Have an unusal entrance into life
2. Be without sin
3. Manifest supernatural in the form of miracles
4. Have an acute sense of difference from other men
5. Speak the greatest words ever spoken
6. Have a lasting and universal influence
7. Satisfy the spiritual hunger in man
8. Exercise power over death

Some of these we may object are necessary in God becoming or manifesting Himself as a human and we might even add some others, but the point is God would be different somehow.  Was Jesus different somehow?
Well, the Bible does record that Jesus performed supernatural acts...miracles yet people might reject this evidence as merely myth or trickery of some sort.  Was Jesus different in any other way?  The Bible also claims Jesus was born of a virgin (a woman who had no sexual relations with a man). Is 7:14, Matt 1:18,24-25, Lk 1:26-35.  Perhaps someone would object and claim this too could have been a concocted tale.