Jesus does never refer to himself as the son of god.
"But what about you?" he asked. "Who do you say I am?"
Simon Peter answered, "You are the Christ, the Son of the living God."
Jesus replied, "Blessed are you, Simon son of Jonah, for this was not revealed to you by man, but by my Father in heaven." - Matthew 16:15-17 (NIV)
The high priest said to him, "I charge you under oath by the living God: tell us if you are the Christ, the Son of God."
"Yes, it is as you say," Jesus replied. - Matthew 26:63b-64a (NIV)
"No one has ever gone into heaven except the one who came from heaven, the Son of Man [...] For God so loved the world that he gave his one and only Son..." - John 3:13, 16a (NIV)
"Why do you accuse me of blasphemy because I said I am God's Son?" - John 10:36b (NIV)
"My Father, who you claim as your God, is the one who glorifies me." - John 8:54 (NIV)
The NIV cleans up John 10 as "God's Son". If you want to quibble over semantics, the KJV says "Son of God". Yes, Jesus also refers to himself as the Son of Man, a term which speaks of his dual-existance: God born into the form of a mortal. The two terms are not mutually exclusive, but different facets of the same being.
The Trinity is cleared spelled out in the end of Matthew in the "Great Commission": Go forth and make disciples of all nations, baptising them in the name of the Father, the Son and the Holy Spirit. The concept of the Trinity is simple: God exists in three parts -- God in Heaven, God on earth (divine - the Holy Spirit), and God on earth (mortal - Jesus). God decides to bring Jesus into the world. Mary is made pregnant when the Holy Spirit comes upon her. Mary gives birth to Jesus, the Son of God & Man. There's no special "power" to it being the Trinity except that the NT holds over Judaic numerology where "3" is a divine number. Certainly there's nothing unbiblical about recognizing the Father, Son and Holy Spirit since Jesus himself calls it so.
EDIT: uBB clean-up
Edited, Wed Jun 30 20:45:20 2004 by Jophiel