What does the Bible say about God being a different type of being than man? Most Christians believe God and man are different types of being (Mormons are a notable exception). What passages in the Bible support this? Or is it inferred by the doctrine of the Trinity and the doctrine of only one God?
God is certainly higher than man. This passage from Isaiah spells it out quite clearly.


  Isaiah 55:8-9 (ESV)
   8 For my thoughts are not your thoughts,
  &nbsp;&nbsp;&nbsp;neither are your ways my ways, declares the LORD.
   9  For as the heavens are higher than the earth,
  &nbsp;&nbsp;&nbsp;so are my ways higher than your ways
  &nbsp;&nbsp;&nbsp;and my thoughts than your thoughts.   


Of course, being higher doesn't necessarily imply being different. But we have further proof in that God is omnipotent and omniscient.


  Genesis 17:1 (ESV)
  When Abram was ninety-nine years old the LORD appeared to Abram and said to him, "I am God Almighty; walk before me, and be blameless,   
  
  Matthew 6:4 (ESV)
   4 so that your giving may be in secret. And your Father who sees in secret will reward you.   
  
  Acts 2:23 (ESV)
   23 this Jesus, delivered up according to the definite plan and foreknowledge of God, you crucified and killed by the hands of lawless men.   


One might still nitpick that omnipotence and omniscience are attributes and don't require being a different type of being. The final point is that God was the first one (as He was before the world and there is only one God). But, one could argue, does the order of existence imply being a different type of being?

I think it's quite obvious that God is a different type of being than man. 

But that's arguable—it depends on how the types of beings are defined, i.e. the chosen taxonomy. Similarly, men and natural satellites are quite different, but you could come up with a  classification that puts them into the same class.